More articles are added to the subdirectory of Physics.

http://knol.google.com/k/narayana-rao-kvss/knol-sub-directory-physics-interesting/2utb2lsm2k7a/1446#

## Tuesday, August 18, 2009

## Friday, July 31, 2009

### Hubble Space Telescope - A Knol Useful to Know More about Optical Instruments

Selected Passages from the Article about Hubble Telescope

The Hubble Space Telescope was launched in 1990, a joint project of NASA (the National Aeronautics and Space Administration of the United States) and ESA (the European Space Agency). It carries a 2.4-m (94-inch) telescope that feeds several different instruments. It is in low Earth orbit, allowing it to be reached and serviced by astronauts, a process that made it work properly in the first place and that continues to allow its updating.

History of Hubble

The Hubble Space Telescope is the descendant of a planned Large Space Telescope, but during the 1980's it was downsized in planning both for psychological reasons, so the word "Large" wouldn't go in the proposal to Congress, and to allow it to fit in the payload bay of a space shuttle. Lyman Spitzer of Princeton University and John Bahcall of the Institute for Advanced Study, also located in Princeton, were principal scientists who worked not only scientifically but also politically to see the project advance.

The mirror was made by the Perkin-Elmer Company in Connecticut, and was said to be the most perfectly and smoothly shaped telescope mirror ever. The telescope mirror was completed and the telescope almost ready to be launched when the space-shuttle Challenger exploded in 1984. With space-shuttle launches suspended, the telescope was put into storage.

For diagrams please visit the source knol.

The telescope was launched on April 24, 1990, from Cape Canaveral on a space shuttle. It was named after Edwin P. Hubble, the astronomer at the Palomar Observatory who had discovered the important cosmological law about the expansion of the Universe, linking its rate of expansion linearly with distance. It received the name in recognition of the prospectively important cosmological work the telescope could do, and in the hope that it could refine Hubble's Law—in particular, Hubble's constant, the constant of proportionality between redshift and distance—to a higher accuracy than had been previously possible.

Science with Hubble

The Hubble Space Telescope has been used by astronomers to study objects in the Universe near and far, excepting only the Sun (which is too bright, but which was indeed detected through the back of the mirror!). A main reason for the launch of Hubble is that from its perch outside Earth's atmosphere, it can have resolution about 7 times finer than normal ground-based resolution from good telescope sites; that is, it can see detail about 7 times finer. It had often been loosely said that it could therefore see 7 times farther into space, but large ground-based telescopes had already been observing objects so far in the outer solar system that it was impossible to see 7 times farther.

In the years since Hubble's launch, ground-based capabilities have advanced, and Active Optics has allowed Hubble's resolution to be achieved in certain limited but growing circumstances from ground-based telescopes. Still, Hubble can attain its high resolution for all objects it observes without complicated post-processing.

Note, however, that Hubble is only one 2.4-m telescope, not large by today's standards. The twin Keck telescopes in Hawaii, for example, have mirrors each 10 m in diameter, about 4 times in diameter and 16 times in area compared with Hubble's. Thus many astronomical projects, particularly those that require collecting as much light as possible, are better carried out with this new generation of large, mountain-based telescopes, still leaving many, many projects best achieved with the high-resolution of Hubble.

Source

Hubble Space Telescope By Jay M. Pasachoff, Astronomer,Williams College, Williamstown, MA, and Chair of the International Astronomical Union's Working Group on Solar Eclipses

http://knol.google.com/k/jay-m-pasachoff/hubble-space-telescope/2vj7b2e7cti8y/1

The knol is under Creative Commons Attribution 3.0 License on 31.7.2009

You can also visit

http://hubblesite.org

The Hubble Space Telescope was launched in 1990, a joint project of NASA (the National Aeronautics and Space Administration of the United States) and ESA (the European Space Agency). It carries a 2.4-m (94-inch) telescope that feeds several different instruments. It is in low Earth orbit, allowing it to be reached and serviced by astronauts, a process that made it work properly in the first place and that continues to allow its updating.

History of Hubble

The Hubble Space Telescope is the descendant of a planned Large Space Telescope, but during the 1980's it was downsized in planning both for psychological reasons, so the word "Large" wouldn't go in the proposal to Congress, and to allow it to fit in the payload bay of a space shuttle. Lyman Spitzer of Princeton University and John Bahcall of the Institute for Advanced Study, also located in Princeton, were principal scientists who worked not only scientifically but also politically to see the project advance.

The mirror was made by the Perkin-Elmer Company in Connecticut, and was said to be the most perfectly and smoothly shaped telescope mirror ever. The telescope mirror was completed and the telescope almost ready to be launched when the space-shuttle Challenger exploded in 1984. With space-shuttle launches suspended, the telescope was put into storage.

For diagrams please visit the source knol.

The telescope was launched on April 24, 1990, from Cape Canaveral on a space shuttle. It was named after Edwin P. Hubble, the astronomer at the Palomar Observatory who had discovered the important cosmological law about the expansion of the Universe, linking its rate of expansion linearly with distance. It received the name in recognition of the prospectively important cosmological work the telescope could do, and in the hope that it could refine Hubble's Law—in particular, Hubble's constant, the constant of proportionality between redshift and distance—to a higher accuracy than had been previously possible.

Science with Hubble

The Hubble Space Telescope has been used by astronomers to study objects in the Universe near and far, excepting only the Sun (which is too bright, but which was indeed detected through the back of the mirror!). A main reason for the launch of Hubble is that from its perch outside Earth's atmosphere, it can have resolution about 7 times finer than normal ground-based resolution from good telescope sites; that is, it can see detail about 7 times finer. It had often been loosely said that it could therefore see 7 times farther into space, but large ground-based telescopes had already been observing objects so far in the outer solar system that it was impossible to see 7 times farther.

In the years since Hubble's launch, ground-based capabilities have advanced, and Active Optics has allowed Hubble's resolution to be achieved in certain limited but growing circumstances from ground-based telescopes. Still, Hubble can attain its high resolution for all objects it observes without complicated post-processing.

Note, however, that Hubble is only one 2.4-m telescope, not large by today's standards. The twin Keck telescopes in Hawaii, for example, have mirrors each 10 m in diameter, about 4 times in diameter and 16 times in area compared with Hubble's. Thus many astronomical projects, particularly those that require collecting as much light as possible, are better carried out with this new generation of large, mountain-based telescopes, still leaving many, many projects best achieved with the high-resolution of Hubble.

Source

Hubble Space Telescope By Jay M. Pasachoff, Astronomer,Williams College, Williamstown, MA, and Chair of the International Astronomical Union's Working Group on Solar Eclipses

http://knol.google.com/k/jay-m-pasachoff/hubble-space-telescope/2vj7b2e7cti8y/1

The knol is under Creative Commons Attribution 3.0 License on 31.7.2009

You can also visit

http://hubblesite.org

### Want to know more about music - Piano Chords

Piano Chords -- How They Are Formed & How They WorkChords: The Harmonic Background Of Melody

A chord is any group of 3 or more notes that are played at the same time. Broken chords, also known as arpeggios, are chords which are played one note at a time, but add up to 3 or more notes.

Chords are made from scales.

A scale is simply a row of notes in some consistent pattern. The word “scale” comes from a Latin word meaning “ladder” – notes ascend or descend the ladder rung by rung.

The notes of all 12 major scales according to their position in the scale is given as a diagram in the knol

http://knol.google.com/k/duane-shinn/piano-chords-how-they-are-formed-how/189kon8274mv1/3#

Visit the article to know more about Piano Chords

Knol is available on Creative Commons Attribution 3.0 License on 31.7.2009

A chord is any group of 3 or more notes that are played at the same time. Broken chords, also known as arpeggios, are chords which are played one note at a time, but add up to 3 or more notes.

Chords are made from scales.

A scale is simply a row of notes in some consistent pattern. The word “scale” comes from a Latin word meaning “ladder” – notes ascend or descend the ladder rung by rung.

The notes of all 12 major scales according to their position in the scale is given as a diagram in the knol

http://knol.google.com/k/duane-shinn/piano-chords-how-they-are-formed-how/189kon8274mv1/3#

Visit the article to know more about Piano Chords

Knol is available on Creative Commons Attribution 3.0 License on 31.7.2009

### Sound and its measurement

NATURE OF SOUND

Origin of sound

Sound is a variation in the pressure of the air of a type which has an effect on our ears and brain. These pressure variations transfer energy from a source of vibration that can be naturally-occurring, such as by the wind or produced by humans such as by speech. Sound in the air can be caused by a variety of vibrations, such as the following.

Moving objects: examples include loudspeakers, guitar strings, vibrating walls and human vocal chords.

Moving air: examples include horns, organ pipes, mechanical fans and jet engines.

A vibrating object compresses adjacent particles of air as it moves in one direction and leaves the particles of air ‘spread out’ as it moves in the other direction. The displaced particles pass on their extra energy and a pattern of compressions and rarefactions travels out from the source, while the individual particles return to their original positions.

In addition to its link with human hearing the term sound is also used for other movement in air governed by similar physical principles. Disturbances in the air with frequencies of vibration which are too low (infrasound) or too high (ultrasound) to be heard by human hearing are also regarded as sound. Other sound terms in common usage include: underwater sound, sound in solids, or structure-borne sound.

Infrasound: frequency too low for human hearing

Ultrasound: frequency too high for human hearing

Wave motion

The mechanical vibrations of sound move forward using wave motion. This means that, although the individual particles of material such as air molecules return to their original position, the sound energy obviously travels forward. The front of the wave spreads out equally in all directions unless it is affected by an object or by another material in its path. The sound waves can travel through solids, liquids and gases, but not through a vacuum.

It is difficult to depict a longitudinal wave in a diagram so it is often convenient to represent a sound waves as a plot against time of the vibrations. The vibrations can be throught of as the movements of the souce of sound, such as a vibrating loudspeaker, or as the movements of a particle of air. For a pure sound of one frequency, as shown, the plot takes the smooth and regular form of a sine wave.

For diagram visit the source

Sound waves are like any other wave motion and therefore can be specified in terms of wavelength, frequency and velocity.

Wavelength

Wavelength (l) is the distance between any two repeating points on a wave. The unit is the metre (m)

Frequency

Frequency (f) is the number of cycles of vibration per second. The unit is the hertz (Hz)

Velocity

Velocity (v) is the distance moved per second in a fixed direction. The unit is metres per second (m/s)

For every vibration of the sound source the wave moves forward by one wavelength. The length of one wavelength multiplied by the number of vibrations per second therefore gives the total length the wave motion moves in 1 second. This total length per second is also the velocity. This relationship between velocity, frequency and wavelength is true for all wave motions and can be written as the formula.

n =f ´ l

where v = velocity in m/s

f = frequency in Hz

l = wavelength in m

The velocity of sound, for any particular material, stays constant. Therefore any increase in freqency, for example, is matched by a decrease in wavelength.

Velocity of sound

A sound wave travels away from its source with a speed of 344 m/s (770 miles per hour) when measured in dry air at 20 °C (68 °F) . This is a respectable speed within a room but slow enough over the ground for us to notice the delay between seeing a source of sound, such as a distant firework, and later hearing the explosion.

The velocity of sound is independent of the rate at which the sound vibrations occur, which means that the frequency of a sound does not affect its speed. The velocity is also unaffected by variations in atmospheric pressure such as those caused by the weather.

But the velocity of sound is affected by the properties of the material through which it is travelling, and the table gives an indication of the velocities of sound in different materials.

The velocity of sound in gases decreases with increasing density as, when the molecules are heavier, then they move less readily. Moist air contains a greater number of light molecules and therefore sound travels slightly faster in moist humid air.

Sound travels faster in liquids and solids than it does in air because of the effect of density and elasticity of those materials. The particles of such materials respond to vibrations more quickly and so convey the pressure vibrations at a faster rate. For example, steel is very elastic and sound travels through steel about 14 times faster than it does through air.

Table of Velocity of sound

Material

Typical velocity (m/s)

Air (0°C)

331

Air (20°C)

344

Water (25°C)

1498

Pine

3300

Glass

5000

Steel

5000

Granite

6000

Frequency of sound

If an object that produces sound waves vibrates 100 times a second, for example, then the frequency of that sound wave will be 100 Hz. The human ear hears this as sound of a certain pitch.

Pitch is the frequency of a sound as perceived by human hearing.

Low-pitched notes are caused by low-frequency sound waves and high-pitched notes are caused by high-frequency waves. The pitch of a note determines its position in the musical scale. The frequency range to which the human ear responds is approximately 20 to 20 000 Hz and frequencies of some typical sounds are shown in the figure.

‘bass’ = low frequency

‘treble’ = high frequency

Most sounds contain a combination of many different frequencies and it is usually convenient to measure and analyse them in ranges of frequencies, such as the octave.

An Octave Band is the range of frequencies between any one frequency and double that frequency.

Quality of sound

A pure tone is sound of only one frequency, such as that given by a tuning fork or electronic signal generator. Most sounds heard in everyday life are a mixture of more than one frequency, although a lowest fundamental frequency predominates when a particular ‘note’ is recognisable. This fundamental frequency is accompanied by overtones or harmonics.

Overtones and Harmonics are frequencies equal to whole-number multiples of the fundamental frequency.

For example, the initial overtones of the note with a fundamental of 440 Hertz are as follows:

440 Hz = fundamental or 1st harmonic

880 Hz = 1st overtone or 2nd harmonic

1320 Hz = 2nd overtone or 3rd harmonic etc.

Different voices and instruments are recognised as having a different quality when making the same note. This individual timbre results because different instruments produce different mixtures of overtones that accompany the fundamental. The frequencies of these overtones may well rise to 10 000 Hz or more and their presence is often an important factor in the overall effect of a sound. A telephone, for example, transmits few frequencies above 3000 Hz and the exclusion of the higher overtones noticeably affects reproduction of the voice and of music.

Cancellation of sound

The nature of a sound wave, such as shown in the earlier figure, means that the vibration of the wave has alternate changes in amplitude called phases. If a wave vibration in one direction meets an equal and opposite vibration, then they will cancel. The effect of this phase inversion in sound waves is to produce little or no sound and gives the possibility of ‘cancelling’ noise. This is the principle of Active Noise Reduction (ANR) used in some headsets and aircraft for example.

Resonance

Every object has a natural frequency which is the characteristic frequency at which it tends to vibrate when disturbed. For example, the sound of a metal bar dropped on the floor can be distinguished from a block of wood dropped in the same way. The natural frequency depends upon factors such as the shape, density and stiffness of the object.

Resonance occurs when the natural frequency of an object coincides with the frequency of any vibrations applied to the object. The result of resonance is extra large vibrations at this frequency.

Resonance may occur in many mechanical systems. For instance, it can cause loose parts of a car to rattle at certain speeds when they resonate with the engine vibrations. The swaying of a suspension bridge can resonate with footsteps from walkers. The shattering of a drinking glass has been attributed to resonance of the object with a singer’s top note! Less dramatic, but of practical application in buildings, is that resonance affects the transmission and absorption of sound within partitions and cavities.

MEASUREMENT OF SOUND

Decibels

The uneven sensitivities of the human hearing system lead us to measuring sound by a logarithmic decibel scale which is progressively 'squashed' rather than being a uniform scale. It happens that this is also the way that our hearing perceives sound energy or strength. So the simple energy or pressure measurements of sound are converted to sound level values in decibels (dB) which are easier numbers for humans to understand and relate to. Extra-terrestrial beings, or even your cat, might well prefer the unconverted values!

Sound levels in decibels start with a zero at the threshold of hearing which is the weakest sound that the average human ear can detect Typical effects of sound levels and changes in sound levels are shown in the illustrations. Remember that there is distinct difference between a change in energy and a change in our idea of loudness.

A change in sound level of + or - 10 dB is a useful figure to remember as it makes difference of approximately twice as loud, or half as loud. We have to say 'approximately' as the experience also depends on individual hearing, on the background noise and on the exact frequencies involved. An increase in sound level of 20 dB (10 dB then another 10 dB) will seem four times

For example, there may be a proposal to increase the average sound level of your environment from 60 dB to 70 dB. This seems a relatively small change, after all the scale runs from 0 to 140 but it will make the environment twice as noisy.

The same idea applies to reducing noise. If the manufacturers of a certain machine can reduce the sound level from 90 dB to 80 dB then the machine will sound approximately half as loud as before.

For Table of Decibel scale visit the source

Sound Meters are also explained in the source article in knol.

Visit the source for diagrams and updated versions.

Source:

Sound and its measurement, Randall McMullan

http://knol.google.com/k/randall-mcmullan/sound-and-its-measurement/1hvmbypv7oiib/3#

The article is in Creative Commons Attribution 3.0 License on 31.7.2009

Origin of sound

Sound is a variation in the pressure of the air of a type which has an effect on our ears and brain. These pressure variations transfer energy from a source of vibration that can be naturally-occurring, such as by the wind or produced by humans such as by speech. Sound in the air can be caused by a variety of vibrations, such as the following.

Moving objects: examples include loudspeakers, guitar strings, vibrating walls and human vocal chords.

Moving air: examples include horns, organ pipes, mechanical fans and jet engines.

A vibrating object compresses adjacent particles of air as it moves in one direction and leaves the particles of air ‘spread out’ as it moves in the other direction. The displaced particles pass on their extra energy and a pattern of compressions and rarefactions travels out from the source, while the individual particles return to their original positions.

In addition to its link with human hearing the term sound is also used for other movement in air governed by similar physical principles. Disturbances in the air with frequencies of vibration which are too low (infrasound) or too high (ultrasound) to be heard by human hearing are also regarded as sound. Other sound terms in common usage include: underwater sound, sound in solids, or structure-borne sound.

Infrasound: frequency too low for human hearing

Ultrasound: frequency too high for human hearing

Wave motion

The mechanical vibrations of sound move forward using wave motion. This means that, although the individual particles of material such as air molecules return to their original position, the sound energy obviously travels forward. The front of the wave spreads out equally in all directions unless it is affected by an object or by another material in its path. The sound waves can travel through solids, liquids and gases, but not through a vacuum.

It is difficult to depict a longitudinal wave in a diagram so it is often convenient to represent a sound waves as a plot against time of the vibrations. The vibrations can be throught of as the movements of the souce of sound, such as a vibrating loudspeaker, or as the movements of a particle of air. For a pure sound of one frequency, as shown, the plot takes the smooth and regular form of a sine wave.

For diagram visit the source

Sound waves are like any other wave motion and therefore can be specified in terms of wavelength, frequency and velocity.

Wavelength

Wavelength (l) is the distance between any two repeating points on a wave. The unit is the metre (m)

Frequency

Frequency (f) is the number of cycles of vibration per second. The unit is the hertz (Hz)

Velocity

Velocity (v) is the distance moved per second in a fixed direction. The unit is metres per second (m/s)

For every vibration of the sound source the wave moves forward by one wavelength. The length of one wavelength multiplied by the number of vibrations per second therefore gives the total length the wave motion moves in 1 second. This total length per second is also the velocity. This relationship between velocity, frequency and wavelength is true for all wave motions and can be written as the formula.

n =f ´ l

where v = velocity in m/s

f = frequency in Hz

l = wavelength in m

The velocity of sound, for any particular material, stays constant. Therefore any increase in freqency, for example, is matched by a decrease in wavelength.

Velocity of sound

A sound wave travels away from its source with a speed of 344 m/s (770 miles per hour) when measured in dry air at 20 °C (68 °F) . This is a respectable speed within a room but slow enough over the ground for us to notice the delay between seeing a source of sound, such as a distant firework, and later hearing the explosion.

The velocity of sound is independent of the rate at which the sound vibrations occur, which means that the frequency of a sound does not affect its speed. The velocity is also unaffected by variations in atmospheric pressure such as those caused by the weather.

But the velocity of sound is affected by the properties of the material through which it is travelling, and the table gives an indication of the velocities of sound in different materials.

The velocity of sound in gases decreases with increasing density as, when the molecules are heavier, then they move less readily. Moist air contains a greater number of light molecules and therefore sound travels slightly faster in moist humid air.

Sound travels faster in liquids and solids than it does in air because of the effect of density and elasticity of those materials. The particles of such materials respond to vibrations more quickly and so convey the pressure vibrations at a faster rate. For example, steel is very elastic and sound travels through steel about 14 times faster than it does through air.

Table of Velocity of sound

Material

Typical velocity (m/s)

Air (0°C)

331

Air (20°C)

344

Water (25°C)

1498

Pine

3300

Glass

5000

Steel

5000

Granite

6000

Frequency of sound

If an object that produces sound waves vibrates 100 times a second, for example, then the frequency of that sound wave will be 100 Hz. The human ear hears this as sound of a certain pitch.

Pitch is the frequency of a sound as perceived by human hearing.

Low-pitched notes are caused by low-frequency sound waves and high-pitched notes are caused by high-frequency waves. The pitch of a note determines its position in the musical scale. The frequency range to which the human ear responds is approximately 20 to 20 000 Hz and frequencies of some typical sounds are shown in the figure.

‘bass’ = low frequency

‘treble’ = high frequency

Most sounds contain a combination of many different frequencies and it is usually convenient to measure and analyse them in ranges of frequencies, such as the octave.

An Octave Band is the range of frequencies between any one frequency and double that frequency.

Quality of sound

A pure tone is sound of only one frequency, such as that given by a tuning fork or electronic signal generator. Most sounds heard in everyday life are a mixture of more than one frequency, although a lowest fundamental frequency predominates when a particular ‘note’ is recognisable. This fundamental frequency is accompanied by overtones or harmonics.

Overtones and Harmonics are frequencies equal to whole-number multiples of the fundamental frequency.

For example, the initial overtones of the note with a fundamental of 440 Hertz are as follows:

440 Hz = fundamental or 1st harmonic

880 Hz = 1st overtone or 2nd harmonic

1320 Hz = 2nd overtone or 3rd harmonic etc.

Different voices and instruments are recognised as having a different quality when making the same note. This individual timbre results because different instruments produce different mixtures of overtones that accompany the fundamental. The frequencies of these overtones may well rise to 10 000 Hz or more and their presence is often an important factor in the overall effect of a sound. A telephone, for example, transmits few frequencies above 3000 Hz and the exclusion of the higher overtones noticeably affects reproduction of the voice and of music.

Cancellation of sound

The nature of a sound wave, such as shown in the earlier figure, means that the vibration of the wave has alternate changes in amplitude called phases. If a wave vibration in one direction meets an equal and opposite vibration, then they will cancel. The effect of this phase inversion in sound waves is to produce little or no sound and gives the possibility of ‘cancelling’ noise. This is the principle of Active Noise Reduction (ANR) used in some headsets and aircraft for example.

Resonance

Every object has a natural frequency which is the characteristic frequency at which it tends to vibrate when disturbed. For example, the sound of a metal bar dropped on the floor can be distinguished from a block of wood dropped in the same way. The natural frequency depends upon factors such as the shape, density and stiffness of the object.

Resonance occurs when the natural frequency of an object coincides with the frequency of any vibrations applied to the object. The result of resonance is extra large vibrations at this frequency.

Resonance may occur in many mechanical systems. For instance, it can cause loose parts of a car to rattle at certain speeds when they resonate with the engine vibrations. The swaying of a suspension bridge can resonate with footsteps from walkers. The shattering of a drinking glass has been attributed to resonance of the object with a singer’s top note! Less dramatic, but of practical application in buildings, is that resonance affects the transmission and absorption of sound within partitions and cavities.

MEASUREMENT OF SOUND

Decibels

The uneven sensitivities of the human hearing system lead us to measuring sound by a logarithmic decibel scale which is progressively 'squashed' rather than being a uniform scale. It happens that this is also the way that our hearing perceives sound energy or strength. So the simple energy or pressure measurements of sound are converted to sound level values in decibels (dB) which are easier numbers for humans to understand and relate to. Extra-terrestrial beings, or even your cat, might well prefer the unconverted values!

Sound levels in decibels start with a zero at the threshold of hearing which is the weakest sound that the average human ear can detect Typical effects of sound levels and changes in sound levels are shown in the illustrations. Remember that there is distinct difference between a change in energy and a change in our idea of loudness.

A change in sound level of + or - 10 dB is a useful figure to remember as it makes difference of approximately twice as loud, or half as loud. We have to say 'approximately' as the experience also depends on individual hearing, on the background noise and on the exact frequencies involved. An increase in sound level of 20 dB (10 dB then another 10 dB) will seem four times

For example, there may be a proposal to increase the average sound level of your environment from 60 dB to 70 dB. This seems a relatively small change, after all the scale runs from 0 to 140 but it will make the environment twice as noisy.

The same idea applies to reducing noise. If the manufacturers of a certain machine can reduce the sound level from 90 dB to 80 dB then the machine will sound approximately half as loud as before.

For Table of Decibel scale visit the source

Sound Meters are also explained in the source article in knol.

Visit the source for diagrams and updated versions.

Source:

Sound and its measurement, Randall McMullan

http://knol.google.com/k/randall-mcmullan/sound-and-its-measurement/1hvmbypv7oiib/3#

The article is in Creative Commons Attribution 3.0 License on 31.7.2009

## Saturday, July 18, 2009

### Interesting Articles on Physics for Dowload

http://knol.google.com/k/narayana-rao-kvss/knol-sub-directory-physics-interesting/2utb2lsm2k7a/1446#

A list of articles for study and download.

You can search for more articles on knol.

A list of articles for study and download.

You can search for more articles on knol.

## Tuesday, May 26, 2009

### IIT JEE 2011 Physics Study Diary - Ch.4 Forces Day 3

Day 3

4.4 Nuclear Forces

4.5 Weak forces

4.6 Scope of Classical physics

Points to be Noted

Nuclear forces

The alpha particle is a bare nucleus of Helium. It contains two protons and two neutrons. It is a stable object and once created it can remain intact until it is not made to interact with other objects.

The protons in the nucleus will repel each other due to coulomb force and try to break the nucleus. Why does the Coulomb force fail to break the nucleus?

There are forces called nuclear forces and they are exerted only if the interacting particles are protons or neutrons or both. They are largely attractive, but with a short range. They are weaker than the Coulomb force if the separation between particles is more than 10^-14 m. For separation smaller than this the nuclear force is stronger than the Coulomb force and it holds the nucleus stable.

Radioactivity, nuclear energy (fission, fusion) etc. result from nuclear force.

A neutron can change into proton and simultaneously emit an electron and a particle called antinutrino.

A proton can also change into neutron and simultaneously emit a positron (and a neutrino). The forces responsible for these changes are called weak forces. The effect of this force is experienced inside protons and neutrons only.

Physics based on Newton's Laws of motion, Newton's law of gravitation, Maxwell's electromagnetism, laws of thermodynamics and the Lorentz force is called classical physics. The behaviour of all the bodies of linear sizes greater than 10^-6 m are adequately described by classical physics. Grains of sands and rain drops fall into this range as well as heavenly bodies.

But sub atomic particles like atoms, nuclei, and electrons have sizes smaller than 10^-6 m and they are explained by quantum physics.

The mechanics of particles moving at velocity equal to light are explained by relativistic mechanics formulated by Einstein in 1905.

4.4 Nuclear Forces

4.5 Weak forces

4.6 Scope of Classical physics

Points to be Noted

Nuclear forces

The alpha particle is a bare nucleus of Helium. It contains two protons and two neutrons. It is a stable object and once created it can remain intact until it is not made to interact with other objects.

The protons in the nucleus will repel each other due to coulomb force and try to break the nucleus. Why does the Coulomb force fail to break the nucleus?

There are forces called nuclear forces and they are exerted only if the interacting particles are protons or neutrons or both. They are largely attractive, but with a short range. They are weaker than the Coulomb force if the separation between particles is more than 10^-14 m. For separation smaller than this the nuclear force is stronger than the Coulomb force and it holds the nucleus stable.

Radioactivity, nuclear energy (fission, fusion) etc. result from nuclear force.

**Weak forces**A neutron can change into proton and simultaneously emit an electron and a particle called antinutrino.

A proton can also change into neutron and simultaneously emit a positron (and a neutrino). The forces responsible for these changes are called weak forces. The effect of this force is experienced inside protons and neutrons only.

**Scope of classical physics**Physics based on Newton's Laws of motion, Newton's law of gravitation, Maxwell's electromagnetism, laws of thermodynamics and the Lorentz force is called classical physics. The behaviour of all the bodies of linear sizes greater than 10^-6 m are adequately described by classical physics. Grains of sands and rain drops fall into this range as well as heavenly bodies.

But sub atomic particles like atoms, nuclei, and electrons have sizes smaller than 10^-6 m and they are explained by quantum physics.

The mechanics of particles moving at velocity equal to light are explained by relativistic mechanics formulated by Einstein in 1905.

## Monday, May 25, 2009

### IIT JEE Physics Study Diary - Ch.3 Forces - Day 2

Day 2

4.3 Electromagnetic (EM) forces

Ex. 4.1

Points to note

Apart from gravitational force between any two bodies, the particles may exert upon each other electromagnetic forces.

If two particles having charges q1 and q2 are at rest with respect to the observer, the force between them has a magnitude

F = (1/4Ï€Îµ0)(q1q2/r^2)

Where Îµ0 = permittivity of air or vacuum = 8.8549 x 10^-12 C² /N-m²

The quantity (1/4Ï€Îµ0) = 9.0 x 10^9 N-m² /C²

q1, q2 = charges

r distance between q1 and q2

This is called coulomb force and it acts along the line joining the particles.

Atoms are composed of electrons, protons and neutrons.

Each electron has 1.6*10^-19 coulomb of negative charge. Each proton has an equal amount of positive charge.

In atoms, the electrons are bound by the electromagnetic force exerted on them by charge on protons. Even the combination of atoms in molecules are brought about by electromagnetic forces only. A lot of atomic and molecular phenomena result from electromagnetic forces between subatomic particles (for example, theory is put forward that charged mesons are responsible for the stability of nucleus).

Examples of electromagnetic force:

1. Bodies in contact: The contact force between bodies in contact arises out of electromagnetic forces acting between the atoms and molecules of the surfaces of the two bodies. The contact force may have a component parallel to the contact surface. This component is known as friction.

2. Tension in a string: Tension in the string is due to electromagnetic forces between atoms or electrons and protons (free electrons and nucleus in metals).

3. Force due to spring: If a spring has natural length x0 and if it is extended to x, it will exert a force

F = k|x-x0| = k|∆x|

k, the proportionality constant is called the spring constant. This force comes into picture due to the electromagnetic forces between the atoms of the material.

Formulas in the session

F = (1/4Ï€Îµ0)(q1q2/r^2)

Where Îµ0 = permittivity of air or vacuum = 8.8549 x 10^-12 C² /N-m²

The quantity (1/4Ï€Îµ0) = 9.0 x 10^9 N-m² /C²

q1, q2 = charges

r distance between q1 and q2

Each electron has 1.6*10^-19 coulomb of negative charge. Each proton has an equal amount of positive charge.

Force due to spring: If a spring has natural length x0 and if it is extended to x, it will exert a force

F = k|x-x0| = k|∆x|

k, the proportionality constant is called the spring constant.

4.3 Electromagnetic (EM) forces

Ex. 4.1

Points to note

**Electromagnetic force**Apart from gravitational force between any two bodies, the particles may exert upon each other electromagnetic forces.

If two particles having charges q1 and q2 are at rest with respect to the observer, the force between them has a magnitude

F = (1/4Ï€Îµ0)(q1q2/r^2)

Where Îµ0 = permittivity of air or vacuum = 8.8549 x 10^-12 C² /N-m²

The quantity (1/4Ï€Îµ0) = 9.0 x 10^9 N-m² /C²

q1, q2 = charges

r distance between q1 and q2

This is called coulomb force and it acts along the line joining the particles.

Atoms are composed of electrons, protons and neutrons.

Each electron has 1.6*10^-19 coulomb of negative charge. Each proton has an equal amount of positive charge.

In atoms, the electrons are bound by the electromagnetic force exerted on them by charge on protons. Even the combination of atoms in molecules are brought about by electromagnetic forces only. A lot of atomic and molecular phenomena result from electromagnetic forces between subatomic particles (for example, theory is put forward that charged mesons are responsible for the stability of nucleus).

Examples of electromagnetic force:

1. Bodies in contact: The contact force between bodies in contact arises out of electromagnetic forces acting between the atoms and molecules of the surfaces of the two bodies. The contact force may have a component parallel to the contact surface. This component is known as friction.

2. Tension in a string: Tension in the string is due to electromagnetic forces between atoms or electrons and protons (free electrons and nucleus in metals).

3. Force due to spring: If a spring has natural length x0 and if it is extended to x, it will exert a force

F = k|x-x0| = k|∆x|

k, the proportionality constant is called the spring constant. This force comes into picture due to the electromagnetic forces between the atoms of the material.

Formulas in the session

F = (1/4Ï€Îµ0)(q1q2/r^2)

Where Îµ0 = permittivity of air or vacuum = 8.8549 x 10^-12 C² /N-m²

The quantity (1/4Ï€Îµ0) = 9.0 x 10^9 N-m² /C²

q1, q2 = charges

r distance between q1 and q2

Each electron has 1.6*10^-19 coulomb of negative charge. Each proton has an equal amount of positive charge.

Force due to spring: If a spring has natural length x0 and if it is extended to x, it will exert a force

F = k|x-x0| = k|∆x|

k, the proportionality constant is called the spring constant.

## Saturday, May 23, 2009

### Physics Study Diary - Ch. 4 Forces - Day 1

Day 1 Study Plan

4.1 Introduction

4.2 Gravitational forces

Points to Note

Force is an interaction between two objects.

Force is exerted by an object A on another object B.

Force is a vector quantity. Hence if two or more forces act on a particle, we can find the resultant force using laws of vector addition.

The SI unit for measuring the force is called a newton.

If a body A exerts a force

Any two bodies attract each other by virtue of their masses.

The force of attraction between two point masses is

F = Gm1m2/r²

where m1 and m2 are the masses of the particles and r is the distance between them.

G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²

The above rule was given for point masses. But it is analytically found that the gravitational force exerted by a spherically symmetric body of mass m1 on another such body of mass m2 kept outside the first body is Gm1m2/r² where r is the distance between the centres of such bodies.

Thus, for the calculation of gravitational force between two spherically symmetric bodies, they can be treated as point masses placed at their centres.

Gravitational force on small bodies by the earth

For earth, the value of radius R and mass M are 6400 km and 6 x 10^24 kg respectively. Hence, the force exerted by earth on a particle of mass m kept at its surface is, F = GMm/R². The direction of this force is towards the centre of the earth.

The quantity GM/R² is a constant and has the dimensions of acceleration.

It is called acceleration due to gravity and is denoted by letter g.

Hence, g and G are different.

Value of g is approximately 9.8 m/s².

In calculations, we often use 10 m/s².

Force exerted on a small body of mass m, kept near the earth's surface is mg in the vertically downward direction.

Gravitational constant is so small that the gravitational force becomes appreciable only when one of the masses has a very large mass.

HC Verma gives the example of Force exerted by a body of 10 kg on another body of 10 kg when they are separted by a distance of 0.5 m. The force comes out to be 2.7*10^-8 N which can hold only 3 microgram. Such forces can be neglected in practice.

Hence we consider only gravitational force exerted by earth.

Formulas

1. F = Gm1m2/r²

where m1 and m2 are the masses of the particles and r is the distance between them.

G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²

2. Force exerted by earth on a particle of mass m kept at its surface is, F = gm/R².

g = approximately 9.8 m/s².

In calculations, we often use 10 m/s²

4.1 Introduction

4.2 Gravitational forces

Points to Note

**Force**Force is an interaction between two objects.

Force is exerted by an object A on another object B.

Force is a vector quantity. Hence if two or more forces act on a particle, we can find the resultant force using laws of vector addition.

The SI unit for measuring the force is called a newton.

**Newton's third law of motion**If a body A exerts a force

**F**on another body B, then B exerts a force**-F**on A,the two forces acting along the same line.**Gravitational force**Any two bodies attract each other by virtue of their masses.

The force of attraction between two point masses is

F = Gm1m2/r²

where m1 and m2 are the masses of the particles and r is the distance between them.

G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²

The above rule was given for point masses. But it is analytically found that the gravitational force exerted by a spherically symmetric body of mass m1 on another such body of mass m2 kept outside the first body is Gm1m2/r² where r is the distance between the centres of such bodies.

Thus, for the calculation of gravitational force between two spherically symmetric bodies, they can be treated as point masses placed at their centres.

Gravitational force on small bodies by the earth

For earth, the value of radius R and mass M are 6400 km and 6 x 10^24 kg respectively. Hence, the force exerted by earth on a particle of mass m kept at its surface is, F = GMm/R². The direction of this force is towards the centre of the earth.

The quantity GM/R² is a constant and has the dimensions of acceleration.

It is called acceleration due to gravity and is denoted by letter g.

Hence, g and G are different.

Value of g is approximately 9.8 m/s².

In calculations, we often use 10 m/s².

Force exerted on a small body of mass m, kept near the earth's surface is mg in the vertically downward direction.

Gravitational constant is so small that the gravitational force becomes appreciable only when one of the masses has a very large mass.

HC Verma gives the example of Force exerted by a body of 10 kg on another body of 10 kg when they are separted by a distance of 0.5 m. The force comes out to be 2.7*10^-8 N which can hold only 3 microgram. Such forces can be neglected in practice.

Hence we consider only gravitational force exerted by earth.

Formulas

1. F = Gm1m2/r²

where m1 and m2 are the masses of the particles and r is the distance between them.

G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²

2. Force exerted by earth on a particle of mass m kept at its surface is, F = gm/R².

g = approximately 9.8 m/s².

In calculations, we often use 10 m/s²

## Friday, May 22, 2009

### IIT JEE 2011 Physics Study Diary - Ch.3 Rest and Motion - Day 5

Rest and Motion

Day 5 study plan

3.9 Change of frame

Ex. 3.10, 3.11

WOE 16,17, 18

Points to Note

The main theme of the section is expressing velocity w.r.t. one Frame into velocity w.r.t. to a different frame

If XOY is one frame called S and X'O'Y' is another frame called S' we can express velocity of a body B w.r.t. S as a combination of velocity of body w.r.t. to S' and velocity of S' w.r.t to S.

Where

we can rewrite above equation as

We can interpret the above equation in terms of two bodies. Assume S', and B are two bodies. If we know velocities of two bodies with respect to a common frame (in this case S)we can find the velocity of one body with respect to the other body (V(B,S')

The above expressions for velocity were derived from the relation between position vectors of the body w.r.t. to S and S' and position vector of origin of S' with respect to origin of S.

Differentiating the position vectors with respect to gives respective velocity

Formulas covered in the session

26.

Where

27.

Where

we can rewrite above equation as

28.

Day 5 study plan

3.9 Change of frame

Ex. 3.10, 3.11

WOE 16,17, 18

Points to Note

The main theme of the section is expressing velocity w.r.t. one Frame into velocity w.r.t. to a different frame

If XOY is one frame called S and X'O'Y' is another frame called S' we can express velocity of a body B w.r.t. S as a combination of velocity of body w.r.t. to S' and velocity of S' w.r.t to S.

**V**(B,S) =**V**(B,S')+**V**(S',S)Where

**V**(B,S) = velocity of body w.r.t to S**V**(B,S') = velocity of body w.r.t to S'**V**(S',S) = velocity of S' w.r.t to Swe can rewrite above equation as

**V**(B,S') =**V**(B,S)-**V**(S',S)We can interpret the above equation in terms of two bodies. Assume S', and B are two bodies. If we know velocities of two bodies with respect to a common frame (in this case S)we can find the velocity of one body with respect to the other body (V(B,S')

The above expressions for velocity were derived from the relation between position vectors of the body w.r.t. to S and S' and position vector of origin of S' with respect to origin of S.

**r**(B,S) =**r**(B,S')+**r**(S',S)Differentiating the position vectors with respect to gives respective velocity

Formulas covered in the session

26.

**r**(B,S) =**r**(B,S')+**r**(S',S)Where

**r**(B,S) = Position vector**r**(B,S') = Position vector**r**(S',S) = Position vector27.

**V**(B,S) =**V**(B,S')+**V**(S',S)Where

**V**(B,S) = velocity of body wrt to S)**V**(B,S') = velocity of body wrt to S')**V**(S',S) = velocity of S' wrt to S)we can rewrite above equation as

28.

**V**(B,S') =**V**(B,S)-**V**(S',S)## Thursday, May 21, 2009

### IIT JEE 2011 Physics Study Diary - Ch.3 Rest and Motion - Day 4

Day 4 - Study Plan

3.7 Motion in a plane

Ex. 3.8

3.8 Projectile motion

Ex. 3.9

WOE 11,12, 14

Points to Note

Motion in plane is described by x coordinate and y coordinate, if we choose X-Y plane. You can imagine time t is on the third axis.

The position of the particle or the body can be described by x and y coordinates.

Displacement during time period t to t+Î”t can be represented by Î”r

Î”

Then Î”

Taking the limits as Î”t tends to zero

v = dr/dt = (dx/dt)i+(dy/dt)j ... (3.15)

Hence x component of velocity is dx/dt

The x-coordinate, the x component of velocity, and the x component of acceleration are related by equations of straight line motion along X axis.

Similarly y components.

Projectile motion is an important example of motion in a plane.

What is a projectile? When a particle is thrown obliquely near the earth's surface, it is called a projectile. It moves along a curved path. If we assume the particle is close to the earth and negligible air resistance to the motion of the particle, the acceleration of the particle will be constant. We solve projectile problems with the assumption that acceleration is constant.

Vertical motion of the projectile is the motion along Y axis and horizontal motion is motion along X axis.

Terms used in describing projectile motion

Point of projection

Angle of projection

Horizontal range

Time of flight

Maximum height reached

The motion of projectile can be discussed separately for the horizontal and vertical parts.

The origin is taken as the point of projection.

The instant the particle is projected is taken as t = 0.

X-Y plane is the plane of motion.

The horizontal line OX is taken as the X axis.

Vertical line OY is the Y axis.

Vertically upward direction is taken as positive direction of Y

Initial velocity of the particle = u

Angle between the velocity and horizontal axis = Î¸

ux – x-component of velocity = u cos Î¸

ax – x component of acceleration = 0

uy – y component of velocity = u sin Î¸

ay = y component of acceleration = -g

Horizontal motion of the projectile – Equations of motion

ux = u cos Î¸

ax = 0

vx = ux +axt = ux = u cos Î¸ (as ax = 0)

Hence x component of the velocity remains constant.

Displacement in horizontal direction = x = uxt+1/2ax t²

As ax = 0, x = ux t = ut cos Î¸

Vertical motion – Equations of motion

uy = u sin Î¸

ay = -g

vy = uy – gt

Displacement in y direction = y = uyt – ½ gt²

vy² = uy² - 2gy

22. Time of flight of the projectile = (2u sin Î¸)/g

23. OB = (u²sin 2Î¸)/g

24. t = (u sin Î¸)/g

At t vertical component of velocity is zero.

25. Maximum height reached by the projectile = (u² sin²Î¸)/2g

3.7 Motion in a plane

Ex. 3.8

3.8 Projectile motion

Ex. 3.9

WOE 11,12, 14

Points to Note

**Motion in a plane**Motion in plane is described by x coordinate and y coordinate, if we choose X-Y plane. You can imagine time t is on the third axis.

The position of the particle or the body can be described by x and y coordinates.

**r**= x**i**= y**j**Displacement during time period t to t+Î”t can be represented by Î”r

Î”

**r**= Î”x**i**= Î”y**j**Then Î”

**r**/Î”t = (Î”x/Î”t)**i**= (Î”y/Î”t)**j**Taking the limits as Î”t tends to zero

v = dr/dt = (dx/dt)i+(dy/dt)j ... (3.15)

Hence x component of velocity is dx/dt

The x-coordinate, the x component of velocity, and the x component of acceleration are related by equations of straight line motion along X axis.

Similarly y components.

**Projectile**Projectile motion is an important example of motion in a plane.

What is a projectile? When a particle is thrown obliquely near the earth's surface, it is called a projectile. It moves along a curved path. If we assume the particle is close to the earth and negligible air resistance to the motion of the particle, the acceleration of the particle will be constant. We solve projectile problems with the assumption that acceleration is constant.

Vertical motion of the projectile is the motion along Y axis and horizontal motion is motion along X axis.

Terms used in describing projectile motion

Point of projection

Angle of projection

Horizontal range

Time of flight

Maximum height reached

The motion of projectile can be discussed separately for the horizontal and vertical parts.

The origin is taken as the point of projection.

The instant the particle is projected is taken as t = 0.

X-Y plane is the plane of motion.

The horizontal line OX is taken as the X axis.

Vertical line OY is the Y axis.

Vertically upward direction is taken as positive direction of Y

Initial velocity of the particle = u

Angle between the velocity and horizontal axis = Î¸

ux – x-component of velocity = u cos Î¸

ax – x component of acceleration = 0

uy – y component of velocity = u sin Î¸

ay = y component of acceleration = -g

Horizontal motion of the projectile – Equations of motion

ux = u cos Î¸

ax = 0

vx = ux +axt = ux = u cos Î¸ (as ax = 0)

Hence x component of the velocity remains constant.

Displacement in horizontal direction = x = uxt+1/2ax t²

As ax = 0, x = ux t = ut cos Î¸

Vertical motion – Equations of motion

uy = u sin Î¸

ay = -g

vy = uy – gt

Displacement in y direction = y = uyt – ½ gt²

vy² = uy² - 2gy

22. Time of flight of the projectile = (2u sin Î¸)/g

23. OB = (u²sin 2Î¸)/g

24. t = (u sin Î¸)/g

At t vertical component of velocity is zero.

25. Maximum height reached by the projectile = (u² sin²Î¸)/2g

## Wednesday, May 20, 2009

### IIT JEE Physics Study Diary - Ch.3 Rest and Motion - Day 3

Day 3 Study Plan

3.6 Motion in a straight line

Ex. 3.5.3.6, 3.7

WOE 3,4,5,6,

Points to Note

As the motion is constrained to move on a straight line, choose the straight line in which motion is taking place as X-axis. Hence x represent the position of the particle at any time instant t. If you want you can imagine a graph between t and x but now t in on the vertical axis and x is on the horizontal axis.

Generally origin is taken at the point where the particle is situated at time t = 0.

Position of the particle at time t is given by x and also x measures displacement (not distance).

Velocity is v = dx/dt (3.9)

acceleration is a = dv/dt (3.10)

a = d²x/dt² (3.11)

Decelaration

If acceleration is negative, then it is along the negative X-axis. It is called deceleration

Motion with constant acceleration

Using integration the formulas for v velocity at any instant, x position at any instant and relation between v,u,x and a are derived in this section.

If acceleration is constant dv/dt = a (constant)

initial velocity = u (at time t =0)

final velocity = v (at time t)

Then v = u+at (3.12)

x = distance moved in time t = ut+½at² (3.13)

Also v² = u²+2ax (3.14)

u,v, and a as well as may take negative or positive values. When u, v and a are negative it shows velocity or acceleration is in the negative X direction.

Example 3.5

a) The question asked is distance travelled. The expression for x gives only displacement. But the remark is that as the particle does not turn back it is equal to distance travelled. Be careful when initial velocity is positive and the acceleration is negative.

Example 3.6

There was a past JEE question which is based on the variable defined in the example.

Freely falling bodies

In this case take the Y axis as the straight line on which the particle or body is moving.

You can take height above the ground as +y and work out the problems.

You can take the starting position of the body as the origin and work out the problem.

The choice may be yours or some choice may be more appropriate in case of some problems, be clear of the formula that you have to use depending on the choice you made.

g is approximately equal to 9.8 m/s², but for convenience in many problems it is given as 10m/s².

3.6 Motion in a straight line

Ex. 3.5.3.6, 3.7

WOE 3,4,5,6,

Points to Note

**Motion in a straight line**As the motion is constrained to move on a straight line, choose the straight line in which motion is taking place as X-axis. Hence x represent the position of the particle at any time instant t. If you want you can imagine a graph between t and x but now t in on the vertical axis and x is on the horizontal axis.

Generally origin is taken at the point where the particle is situated at time t = 0.

Position of the particle at time t is given by x and also x measures displacement (not distance).

Velocity is v = dx/dt (3.9)

acceleration is a = dv/dt (3.10)

a = d²x/dt² (3.11)

Decelaration

If acceleration is negative, then it is along the negative X-axis. It is called deceleration

Motion with constant acceleration

Using integration the formulas for v velocity at any instant, x position at any instant and relation between v,u,x and a are derived in this section.

If acceleration is constant dv/dt = a (constant)

initial velocity = u (at time t =0)

final velocity = v (at time t)

Then v = u+at (3.12)

x = distance moved in time t = ut+½at² (3.13)

Also v² = u²+2ax (3.14)

u,v, and a as well as may take negative or positive values. When u, v and a are negative it shows velocity or acceleration is in the negative X direction.

Example 3.5

a) The question asked is distance travelled. The expression for x gives only displacement. But the remark is that as the particle does not turn back it is equal to distance travelled. Be careful when initial velocity is positive and the acceleration is negative.

Example 3.6

There was a past JEE question which is based on the variable defined in the example.

Freely falling bodies

In this case take the Y axis as the straight line on which the particle or body is moving.

You can take height above the ground as +y and work out the problems.

You can take the starting position of the body as the origin and work out the problem.

The choice may be yours or some choice may be more appropriate in case of some problems, be clear of the formula that you have to use depending on the choice you made.

g is approximately equal to 9.8 m/s², but for convenience in many problems it is given as 10m/s².

### Physics Study Diary for IIT JEE - Ch.3 Rest and Motion - Day 2

Plan for Day 2

4. Average velocity and instantaneous velocity

Ex. 3.4

Worked out example 2

3.5 Average accleration and instantaneous aceleration

WOE 3 to 4

Exercises: 1 to 5

Points to Note

Average velocity

Average speed and average velocity of a body over a specified time interval may not turnout to be same.

Example See the worked out example 2 of HC Verma's book.

The teacher made 10 rounds back and forth in the room and the total distance moved is 800 feet (10 rounds back and forth of 40 ft room). As the time taken is 50 minutes, average speed is 800/50 = 16ft/min.

But because he went out of the same door that he has entered, displacement is zero and hence average velocity is zero.

Instantaneous velocity

Average acceleration

Instantaneous acceleration

Position Vector: If we join the origin to the position of a particle by a straight line and put an arrow towards the position of the particle, we get the position vector of the particle.

If the particle moves from position A to position B, we can define position vector of A and position vector of B and OB - OA will give displacement ( a vector quantity).

Another point to note: slope of velocity-time diagram gives the instant acceleration at that point.

4. Average velocity and instantaneous velocity

Ex. 3.4

Worked out example 2

3.5 Average accleration and instantaneous aceleration

WOE 3 to 4

Exercises: 1 to 5

Points to Note

Average velocity

Average speed and average velocity of a body over a specified time interval may not turnout to be same.

Example See the worked out example 2 of HC Verma's book.

The teacher made 10 rounds back and forth in the room and the total distance moved is 800 feet (10 rounds back and forth of 40 ft room). As the time taken is 50 minutes, average speed is 800/50 = 16ft/min.

But because he went out of the same door that he has entered, displacement is zero and hence average velocity is zero.

Instantaneous velocity

Average acceleration

Instantaneous acceleration

Position Vector: If we join the origin to the position of a particle by a straight line and put an arrow towards the position of the particle, we get the position vector of the particle.

If the particle moves from position A to position B, we can define position vector of A and position vector of B and OB - OA will give displacement ( a vector quantity).

Another point to note: slope of velocity-time diagram gives the instant acceleration at that point.

## Monday, May 18, 2009

### Physics Study Diary for IIT JEE 2011 - Ch.3 Rest and Motion

I am planning to study the Physics chapters as per the study plan that I have given. This study would be of help to me in preparing JEE Level Revision problem set for each chapter.

Today (19.5.2009) I did the following portion

Day 1

3.1 Rest and Motion

3.2 Distance and displacement

Ex. 3.1

3.3 average speed and instantaneous speed

Ex. 3.2,3.3

Worked out examples 1,2

Points to note.

3.1 Rest and Motion

Motion is a combined property of the object under study and the observer. There is no meaning of rest or motion without the viewer.

To identify the rest or motion, we need to locate the position of a particle with respect to a frame of reference. The frame of reference will have three mutually perpendicular axes (X-Y-Z) and the particle can be represented by coordinates x,y,z.

If all coordinates remain unchanged as time passes, we say that particle is at rest. If there is change in any of the coordinates with time, we say the particle or the body represented by the particle is having motion.

I some problems or situations frame of reference is specifically mentioned. Otherwise the frame of reference is understood more easily from the context.

Figure 1: A man with a pistol threatening and asking people not to move.

3.2 Distance and Displacement

If a particle moves from position A to Position B in time t, displacement is the length of the straight line joining A to B. The direction of a vector representing this displacement is from A to B. Displacement is a vector quantity. It has both magnitude and direction.

In the movement between positions A and B the particle may take the path ACB. The length of the path ACB will be distance travelled by the particle. It is only scalar quantity. It has not direction.

3.3 Average speed and Instantaneous speed

The average speed of a particle in a specific time interval is defined as the distance travelled by the particle divided by the time interval.

We can plot the distance s as a function of time. In this graph, the instantaneous speed at time t equals the slope of the tangent at the time t. The average speed in a time interval t to t+Î”t become equal to the slope of the chord Î”s/Î”t. As Î”t becomes approaches zero, this average speed becomes instantaneous speed and ds/dt becomes the instantaneous speed.

If we plot a speed versus time graph ( v versus t), the distance travelled in time t (t1 to t2) will be equal to the area bounded by the curve v = f(t), x axis, and the two ordinates t = t1 and t = t2.

In terms of integration it can be represented as s = ∫vdt from t1 to t2

For study plan for IIT JEE 2011 for the year 2009-10

http://iit-jee-2011.blogspot.com/2009/04/it-jee-2011-annual-study-plan-for.html

Today (19.5.2009) I did the following portion

Day 1

3.1 Rest and Motion

3.2 Distance and displacement

Ex. 3.1

3.3 average speed and instantaneous speed

Ex. 3.2,3.3

Worked out examples 1,2

Points to note.

3.1 Rest and Motion

Motion is a combined property of the object under study and the observer. There is no meaning of rest or motion without the viewer.

To identify the rest or motion, we need to locate the position of a particle with respect to a frame of reference. The frame of reference will have three mutually perpendicular axes (X-Y-Z) and the particle can be represented by coordinates x,y,z.

If all coordinates remain unchanged as time passes, we say that particle is at rest. If there is change in any of the coordinates with time, we say the particle or the body represented by the particle is having motion.

I some problems or situations frame of reference is specifically mentioned. Otherwise the frame of reference is understood more easily from the context.

Figure 1: A man with a pistol threatening and asking people not to move.

3.2 Distance and Displacement

If a particle moves from position A to Position B in time t, displacement is the length of the straight line joining A to B. The direction of a vector representing this displacement is from A to B. Displacement is a vector quantity. It has both magnitude and direction.

In the movement between positions A and B the particle may take the path ACB. The length of the path ACB will be distance travelled by the particle. It is only scalar quantity. It has not direction.

3.3 Average speed and Instantaneous speed

The average speed of a particle in a specific time interval is defined as the distance travelled by the particle divided by the time interval.

We can plot the distance s as a function of time. In this graph, the instantaneous speed at time t equals the slope of the tangent at the time t. The average speed in a time interval t to t+Î”t become equal to the slope of the chord Î”s/Î”t. As Î”t becomes approaches zero, this average speed becomes instantaneous speed and ds/dt becomes the instantaneous speed.

If we plot a speed versus time graph ( v versus t), the distance travelled in time t (t1 to t2) will be equal to the area bounded by the curve v = f(t), x axis, and the two ordinates t = t1 and t = t2.

In terms of integration it can be represented as s = ∫vdt from t1 to t2

For study plan for IIT JEE 2011 for the year 2009-10

http://iit-jee-2011.blogspot.com/2009/04/it-jee-2011-annual-study-plan-for.html

### Nobel Prize Winners in Physics from 1901-1925 - IIT JEE - Extra-curricular Study

Year Physics

1901 RÃ¶ntgen, Wilhelm Conrad

For discovery of X-rays

1902 Lorentz, Hendrik A.

Zeeman, Pieter

1903 Becquerel, Henri;

Curie, Pierre;

Curie, Marie

1904 Rayleigh, Lord

1905 Lenard, Philipp

1906 Thomson, J. J.

1907 Michelson, Albert A.

1908 Lippmann, Gabriel

1909 Braun, Ferdinand

Marconi, Guglielmo

1910 van der Waals, Johannes Diderik

1911 Wien, Wilhelm

1912 DalÃ©n, Gustaf

1913 Onnes, Heike Kamerlingh

1914 von Laue, Max

1915 Bragg, William Henry:

Bragg, William Lawrence

1916 None

1917 Barkla, Charles Glover

1918 Planck, Max

1919 Stark, Johannes

1920 Guillaume, Charles Edouard

1921 Einstein, Albert

1922 Bohr, Niels

1923 Millikan, Robert A.

1924 Siegbahn, Manne

1925 Franck, James

Hertz, Gustav

Sources

http://nobelprize.org/nobel_prizes/physics/laureates/http://history1900s.about.com/library/misc/blnobelphysics.htm

1901 RÃ¶ntgen, Wilhelm Conrad

For discovery of X-rays

1902 Lorentz, Hendrik A.

Zeeman, Pieter

1903 Becquerel, Henri;

Curie, Pierre;

Curie, Marie

1904 Rayleigh, Lord

1905 Lenard, Philipp

1906 Thomson, J. J.

1907 Michelson, Albert A.

1908 Lippmann, Gabriel

1909 Braun, Ferdinand

Marconi, Guglielmo

1910 van der Waals, Johannes Diderik

1911 Wien, Wilhelm

1912 DalÃ©n, Gustaf

1913 Onnes, Heike Kamerlingh

1914 von Laue, Max

1915 Bragg, William Henry:

Bragg, William Lawrence

1916 None

1917 Barkla, Charles Glover

1918 Planck, Max

1919 Stark, Johannes

1920 Guillaume, Charles Edouard

1921 Einstein, Albert

1922 Bohr, Niels

1923 Millikan, Robert A.

1924 Siegbahn, Manne

1925 Franck, James

Hertz, Gustav

Sources

http://nobelprize.org/nobel_prizes/physics/laureates/http://history1900s.about.com/library/misc/blnobelphysics.htm

## Friday, May 15, 2009

### Noble Prize Winners in Physics from 2001 - IIT JEE - Extra-curricular Study

Year - Scientist/Physicist

2001 - Eric A. Cornell, Carl E. Wieman, (US), Wolfgang Ketterle (Germany)

2002 - Riccardo Giacconi, Rayond Davis Jr. (US), Masatoshi Koshiba (Jap)

2003 - Alexei A. Abrikov,(US-Rus), Vitaly I. Ginzburg (Rus). Anthony J. Leggett, (UK-US)

2004 - David J. Gross, H. David Politzer, Frank Wilczek (US)

2005 - Roy glauber, John Hall (both US), and Theodor Haensch (Germany)

2006

2007

2008

2001 - Eric A. Cornell, Carl E. Wieman, (US), Wolfgang Ketterle (Germany)

2002 - Riccardo Giacconi, Rayond Davis Jr. (US), Masatoshi Koshiba (Jap)

2003 - Alexei A. Abrikov,(US-Rus), Vitaly I. Ginzburg (Rus). Anthony J. Leggett, (UK-US)

2004 - David J. Gross, H. David Politzer, Frank Wilczek (US)

2005 - Roy glauber, John Hall (both US), and Theodor Haensch (Germany)

2006

2007

2008

## Sunday, April 19, 2009

### IIT JEE 2010 Syllabus for Physics

IIT JEE 2010 syllabus will be available only when the JEE advertisment is released. You have to prepared using JEE 2009 syllabus up to that time.

## Monday, April 13, 2009

### Memory Maps for IIT JEE Physics - Mental Map

Memory is map linking one concept to another concept. Mind map or mental map helps in your memorizing things.

Let me try to identify main concepts in each chapter and link them to more concepts related to each of them

Chapters from "Concepts of Physics Part I and II" by H C Verma

Chapters

1. Introduction to physics

2. Physics and mathematics

3. Rest and motion :kinematics

Speed - average speed - instantaneous speed

Velocity - Average velocity - instantaneous velocity – Acceleration

Acceleration - Average acceleration - instantaneous acceleration

Motion - straight line - Motion in a plane - Projectile motion

Frame of Reference – Change in Frame of Reference

4. The forces

Gravitational forces - G (universal constant 6.67 *106-11 N-m^2/kg^2) – Acceleration due to gravity g = GM/R^2) - Spherical body treated as a point mass at their centres

Electromagnetic (EM) forces – Coulomb forces – Forces between two surfaces in contact – Tension in a string or rope – Force due to a spring

Nuclear Forces – Exerted when interacting particles are protons or neutrons

Weak forces – Forces responsible for beta decay – antinutrino - positron

Scope of Classical physics – Applicable to bodies of linear sizes greater than 10^-6 m – Subatomic bodies – Quantum physics applicable – If the velocity of bodies are comparable to 3*10^* m/s relativistic mechanics is applicable.

5. Newtons law of motion

Newton's First law – Inertial frame of reference – Earth - Noninertial frame of reference

Newton's second law –( f = ma) - Freebody diagram

Newton's third law of motion – action - reaction

Pseudo forces – inertial forces

Inertia – a property which determines acceleration

6. Friction

Kinetic friction – Opposite to motion – Coefficient of Kinetic friction –

Static friction - Limiting friction – Max. Static friction - Coefficient of static friction

Measurement of friction Coefficients- Horizontal table method – Inclined table method

7. Circular motion

Angular variables – Angular position – Angular velocity – Angular acceleration – tangential acceleration

Unit vectors along the radius and the tangent – Tangential Unit vectors - Radial Unit vectors

Acceleration – Uniform circular motion - Nonuniform circular motion

Effects of earth's rotation – Colatitude – apparent weight

8. Work and energy

Work and energy - Work - Kinetic energy - Work energy theorem - Potential energy - Conservative and nonconservative forces - Gravitational potential energy - Different forms of energy - Mass energy equivalence

Work - Calculation of work done -

Potential energy - Potential energy of a compressed or extended spring - Gravitational potential energy

9. Centre of mass,linear momentum,collision

Centre of mass, linear momentum, collision - Centre of mass - Motion of the Centre of mass - Linear momentum – Collision – Impulse

Centre of mass - Centre of mass of continuous bodies - Motion of the Centre of mass

Linear momentum - Its conservation principle - Rocket propulsion

Collision - Elastic collision in one dimension - Perfectly inelastic collision in one dimension - Coefficient of restitution - Elastic collision in two dimensions

Impulse - Impulsive force

10. Rotational mechanics

11. Gravitation

12. Simple harmonic motion

13. Fluid mechanics

14. Some mechanical properties of matter

15. Wave motion and waves on a string

16. Sound waves

17. Light waves

18. Geometrical optics

19. Optical instruments

20. Dispersion and spectra

21. Speed of light

22. Photometry

23. Heat and Temperature

24. Kinetic theory of Gases

25. Calorimetry

26. Laws of Thermodynamics

27. Specific Heat of Capacities of Gases

28. Heat transfer

29. Electric Field and Potential

30. Gauss's Law

31. Capacitors

32. Electric Current in Conductors

32. Thermal and Chemical effects of Electric Current

33. Thermal and Chemical Effects of Electric Current

34. Magentic Field

35. Magnetic field due to a Current

36. Permanent Magnets

37. Magnetic Properties of Matter

38. Electro Magentic Induction

39. Alternating current

40. electromagentic Waves

41. Electric Current through Gases

42. Photoelectric Effect and Waveparticle Duality

43. Bohr's Model and Physics of Atom

44. X-Rays

45. SemiConductors and Semiconductor Devices

46. Nucleus

47. The Special Theory of Relativity

Let me try to identify main concepts in each chapter and link them to more concepts related to each of them

Chapters from "Concepts of Physics Part I and II" by H C Verma

Chapters

1. Introduction to physics

**Physics**- Understanding nature - Mathematics - Units - Dimensions**Units**- Fundamental quantities - Derived quanties - SI units - SI Prefixes**SI Units**- Metre - Kilogram - Second - Ampere - Kelvin - Mole**Dimension**- Homogenuity - Conversion of Units**Understanding Nature**- Structure of world**Order of magnitude**2. Physics and mathematics

3. Rest and motion :kinematics

**Rest - Motion – displacement – Speed – Velocity – Acceleration – Frame of Reference**

Displacement – Distance movedDisplacement – Distance moved

Speed - average speed - instantaneous speed

Velocity - Average velocity - instantaneous velocity – Acceleration

Acceleration - Average acceleration - instantaneous acceleration

Motion - straight line - Motion in a plane - Projectile motion

Frame of Reference – Change in Frame of Reference

4. The forces

**Forces - Gravitational forces - Electromagnetic (EM) forces - Nuclear Forces - Weak forces - Scope of Classical physics**Gravitational forces - G (universal constant 6.67 *106-11 N-m^2/kg^2) – Acceleration due to gravity g = GM/R^2) - Spherical body treated as a point mass at their centres

Electromagnetic (EM) forces – Coulomb forces – Forces between two surfaces in contact – Tension in a string or rope – Force due to a spring

Nuclear Forces – Exerted when interacting particles are protons or neutrons

Weak forces – Forces responsible for beta decay – antinutrino - positron

Scope of Classical physics – Applicable to bodies of linear sizes greater than 10^-6 m – Subatomic bodies – Quantum physics applicable – If the velocity of bodies are comparable to 3*10^* m/s relativistic mechanics is applicable.

5. Newtons law of motion

**Newtons laws of motion - First law - second law - third law - Pseudo forces - Inertia**Newton's First law – Inertial frame of reference – Earth - Noninertial frame of reference

Newton's second law –( f = ma) - Freebody diagram

Newton's third law of motion – action - reaction

Pseudo forces – inertial forces

Inertia – a property which determines acceleration

6. Friction

**Friction – Normal contact force – Friction - Kinetic friction - Static friction - Laws of friction - Atomic level friction – Rolling Friction**Kinetic friction – Opposite to motion – Coefficient of Kinetic friction –

Static friction - Limiting friction – Max. Static friction - Coefficient of static friction

Measurement of friction Coefficients- Horizontal table method – Inclined table method

7. Circular motion

**Circular motion - Angular variables - Unit vectors along the radius and the tangent – Acceleration - Banking of roads in circular turns - Centrifugal force – Effects of earth's rotation**Angular variables – Angular position – Angular velocity – Angular acceleration – tangential acceleration

Unit vectors along the radius and the tangent – Tangential Unit vectors - Radial Unit vectors

Acceleration – Uniform circular motion - Nonuniform circular motion

Effects of earth's rotation – Colatitude – apparent weight

8. Work and energy

Work and energy - Work - Kinetic energy - Work energy theorem - Potential energy - Conservative and nonconservative forces - Gravitational potential energy - Different forms of energy - Mass energy equivalence

Work - Calculation of work done -

Potential energy - Potential energy of a compressed or extended spring - Gravitational potential energy

9. Centre of mass,linear momentum,collision

Centre of mass, linear momentum, collision - Centre of mass - Motion of the Centre of mass - Linear momentum – Collision – Impulse

Centre of mass - Centre of mass of continuous bodies - Motion of the Centre of mass

Linear momentum - Its conservation principle - Rocket propulsion

Collision - Elastic collision in one dimension - Perfectly inelastic collision in one dimension - Coefficient of restitution - Elastic collision in two dimensions

Impulse - Impulsive force

10. Rotational mechanics

11. Gravitation

12. Simple harmonic motion

13. Fluid mechanics

14. Some mechanical properties of matter

15. Wave motion and waves on a string

16. Sound waves

17. Light waves

18. Geometrical optics

19. Optical instruments

20. Dispersion and spectra

21. Speed of light

22. Photometry

23. Heat and Temperature

24. Kinetic theory of Gases

25. Calorimetry

26. Laws of Thermodynamics

27. Specific Heat of Capacities of Gases

28. Heat transfer

29. Electric Field and Potential

30. Gauss's Law

31. Capacitors

32. Electric Current in Conductors

32. Thermal and Chemical effects of Electric Current

33. Thermal and Chemical Effects of Electric Current

34. Magentic Field

35. Magnetic field due to a Current

36. Permanent Magnets

37. Magnetic Properties of Matter

38. Electro Magentic Induction

39. Alternating current

40. electromagentic Waves

41. Electric Current through Gases

42. Photoelectric Effect and Waveparticle Duality

43. Bohr's Model and Physics of Atom

44. X-Rays

45. SemiConductors and Semiconductor Devices

46. Nucleus

47. The Special Theory of Relativity

## Saturday, April 11, 2009

### Study Plan - Study Guide

I am posting a study plan for each of the chapter. The plan is of 20 days in which first 10 days is for study of the lesson and next 10 days is for revision and solving problems. A candidate must be able to master the chapter in these 20 days by solving every question and problem in the HC Verma text book. By taking a target of 3 chapters in each month for the detailed study 10 days each chapter, candidates can complete each text or one year's portion during the period May to December.

Click on the label HC Verma Study Guide for the plan of various chapters. I completed posting for many chapters of Book 1 and plan to complete for the required number of chapters by May 1.

Click on the label HC Verma Study Guide for the plan of various chapters. I completed posting for many chapters of Book 1 and plan to complete for the required number of chapters by May 1.

## Saturday, March 7, 2009

### Blog status

I started revising the study guides of each chapter by providing a 20 days schedule for the first time study and revision of the chapter. I posted the schedule for the first chapter today. I plan to do similar posting for all the chapters.

## Tuesday, February 10, 2009

### COMPTON EFFECT

Arthur Compton and Debye both provided in 1922 a very simple mathematical framework for the momentum of these photons with Compton having experimental evidence from firing X-Rays of known frequency into graphite and looking at recoil electrons.

Let E = mc² = hf for a photon, where f is frequency, and "m" is the mass "equivalent" of the photon given they have no "rest mass". (It is important to recognise that stopping a photon to measure its mass eliminates it -so it has no "at rest" mass - crucial in Special Relativity where, to travel at the speed of light, mass would otherwise become infinite.)

Having "rigged" this mass problem,

p = momentum = mc (mass x velocity) = hf/c = E/c = h/l

The experiment shows that X-Rays and electrons behave exactly like ball bearings colliding on a table top using the same 2D vector diagrams. They enter the graphite at one wavelength and leave at a longer wavelength as they have transfered both momentum and kinetic energy to an electron. Momentum and energy are conserved in the collision if we accept the equation above for momentum of light.

When the photon enters at l0 and leaves at l1, its energy has changed from E0 to E1 and momentum from E0/c to E1/c with a change in direction of q. The electron gains Ek = E0 - E1

See for a diagram and more details

http://www.launc.tased.edu.au/online/sciences/physics/compton.html

The Compton Effect ( a different explanation)

Convincing evidence that light is made up of particles (photons), and that photons have momentum, can be seen when a photon with energy hf collides with a stationary electron. Some of the energy and momentum is transferred to the electron (this is known as the Compton effect), but both energy and momentum are conserved in this elastic collision. After the collision the photon has energy hf' and the electron has acquired a kinetic energy K.

Conservation of energy: hf = hf' + K

Combining this with the momentum conservation equations, it can be shown that the wavelength of the outgoing photon is related to the wavelength of the incident photon by the equation:

Î”Î» = Î»' - Î» = (h/m

The combination of factors h/m

Source:

http://physics.bu.edu/~duffy/semester2/c35_compton.html

It has problems and examples and demonstration also.

Let E = mc² = hf for a photon, where f is frequency, and "m" is the mass "equivalent" of the photon given they have no "rest mass". (It is important to recognise that stopping a photon to measure its mass eliminates it -so it has no "at rest" mass - crucial in Special Relativity where, to travel at the speed of light, mass would otherwise become infinite.)

Having "rigged" this mass problem,

p = momentum = mc (mass x velocity) = hf/c = E/c = h/l

The experiment shows that X-Rays and electrons behave exactly like ball bearings colliding on a table top using the same 2D vector diagrams. They enter the graphite at one wavelength and leave at a longer wavelength as they have transfered both momentum and kinetic energy to an electron. Momentum and energy are conserved in the collision if we accept the equation above for momentum of light.

When the photon enters at l0 and leaves at l1, its energy has changed from E0 to E1 and momentum from E0/c to E1/c with a change in direction of q. The electron gains Ek = E0 - E1

See for a diagram and more details

http://www.launc.tased.edu.au/online/sciences/physics/compton.html

The Compton Effect ( a different explanation)

Convincing evidence that light is made up of particles (photons), and that photons have momentum, can be seen when a photon with energy hf collides with a stationary electron. Some of the energy and momentum is transferred to the electron (this is known as the Compton effect), but both energy and momentum are conserved in this elastic collision. After the collision the photon has energy hf' and the electron has acquired a kinetic energy K.

Conservation of energy: hf = hf' + K

Combining this with the momentum conservation equations, it can be shown that the wavelength of the outgoing photon is related to the wavelength of the incident photon by the equation:

Î”Î» = Î»' - Î» = (h/m

_{e}c)(1 - cosq)The combination of factors h/m

_{e}c = 2.43 x 10^{-12}m, where m_{e}is the mass of the electron, is known as the Compton wavelength. The collision causes the photon wavelength to increase by somewhere between 0 (for a scattering angle of 0°) and twice the Compton wavelength (for a scattering angle of 180°).Source:

http://physics.bu.edu/~duffy/semester2/c35_compton.html

It has problems and examples and demonstration also.

## Saturday, February 7, 2009

### Schrodinger’s Equation

Quantum mechanics describes the spectra in a much better way than Bohr’s model.

Electron has a wave character as well as a particle character. The wave function of the electron Ïˆ(r,t ) is obtained by solving Schrodinger’s wave equation. The probability of finding an electron is high where | Ïˆ(r,t )|² is greater. Not only the information about the electron’s position but information about all the properties including energy etc. that we calculated using the Bohr’s postulates are contained in the wave function of Ïˆ(r,t).

Quantum Mechanics of the Hydrogen Atom

The wave function of the electron Ïˆ(r,t) is obtained from the Schrodinger’s equation

-(h²/8Ï€²m) [∂²Ïˆ /∂x² + ∂²Ïˆ /∂y² + ∂²Ïˆ/∂z²] - Ze²Ïˆ/4Ï€Îµ

where

(x.y,z ) refers to a point with the nucleus as the origin and r is the distance of this point from the nucleus.

E refers to the energy.

Z is the number of protons.

There are infinite number of functions Ïˆ(r,t) which satisfy the equations.

These functions may be characterized by three parameters n,l, and m

For each combination of n,l, and m

The energy of the wave function of characterized by n,l, and m

En = - mZ²e

These energies are identical with Bohr’s model energies.

The paramer n is called the principal quantum number, l the orbital angular momentum quantum number and m

When n = 1, the wave function of the hydrogen atom is

Ïˆ(r) = Ïˆ

Ïˆ

a

In quantum mechanics, the idea of orbit is invalid. At any instant the wve function is spread over large distances in space, and wherever Ïˆ≠ 0, the presence of electron may be felt.

The probability of finding the electron in a small volume dV is | Ïˆ(r)| ² dV

We can calculate the probability p(r)dr of finding the electron at a distance between r and r+dr from the nucleus.

In the ground state for hydrogen atom it comes out to be

P(r) = (4/ a

The plot of P(r) versus r shows that P(r) is maximum at r = a

But when we put n =2, the maximum probability comes at two radii one near r = a

Electron has a wave character as well as a particle character. The wave function of the electron Ïˆ(r,t ) is obtained by solving Schrodinger’s wave equation. The probability of finding an electron is high where | Ïˆ(r,t )|² is greater. Not only the information about the electron’s position but information about all the properties including energy etc. that we calculated using the Bohr’s postulates are contained in the wave function of Ïˆ(r,t).

Quantum Mechanics of the Hydrogen Atom

The wave function of the electron Ïˆ(r,t) is obtained from the Schrodinger’s equation

-(h²/8Ï€²m) [∂²Ïˆ /∂x² + ∂²Ïˆ /∂y² + ∂²Ïˆ/∂z²] - Ze²Ïˆ/4Ï€Îµ

_{0}r = E Ïˆwhere

(x.y,z ) refers to a point with the nucleus as the origin and r is the distance of this point from the nucleus.

E refers to the energy.

Z is the number of protons.

There are infinite number of functions Ïˆ(r,t) which satisfy the equations.

These functions may be characterized by three parameters n,l, and m

_{l}.For each combination of n,l, and m

_{l}there is an associated unique value of E of the atom of the ion.The energy of the wave function of characterized by n,l, and m

_{l}depends only on n and may be written asEn = - mZ²e

^{4}/8 Îµ_{0}²h²n²These energies are identical with Bohr’s model energies.

The paramer n is called the principal quantum number, l the orbital angular momentum quantum number and m

_{l}. The magnetic quantum number.When n = 1, the wave function of the hydrogen atom is

Ïˆ(r) = Ïˆ

_{100}= √(Z³/ Ï€ a_{0}²) *(e^{-r/ a0})Ïˆ

_{100}denotes that n =1, l = 0 and m_{l}= 0a

_{0}= Bohr radiusIn quantum mechanics, the idea of orbit is invalid. At any instant the wve function is spread over large distances in space, and wherever Ïˆ≠ 0, the presence of electron may be felt.

The probability of finding the electron in a small volume dV is | Ïˆ(r)| ² dV

We can calculate the probability p(r)dr of finding the electron at a distance between r and r+dr from the nucleus.

In the ground state for hydrogen atom it comes out to be

P(r) = (4/ a

_{0})r²e^{-2r/ a0 }The plot of P(r) versus r shows that P(r) is maximum at r = a

_{0}Which the Bohr’s radius.But when we put n =2, the maximum probability comes at two radii one near r = a

_{0}and the other at r = 5.4 a_{0}. According to Bohr model all electrons should be at r = 4 a_{0}.## Thursday, January 1, 2009

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