The idea that all matter is made of very small indivisible particles is very old.

Robert Boyle’s study of compression and expansion of air brings out the idea that air is made of tiny particles with lot of empty space between the particles.

The smallest unit of an element which carries all the properties of the element is called an atom.

Experiments on discharge tube, measurement of e/m by Thomson etc. established the existence of negatively charged electrons in the atoms.

Because atoms are electrically neutral, a search for the positive charge inside the atom was started.

## Monday, November 10, 2008

### Thomson’s Model of the atom

Thomson (1898) suggested that the atom is a positively charged solid sphere in which electrons are embedded in sufficient number to create a neutral atom. This model of the atom could explain why only negatively charged particles are being emitted when a metal is heated. This model was also useful to explain the formation of ions and ionic compounds.

### Lenard's Suggestion on Atomic Structure

Lenard observed that cathode rays are passing through thin material without any deviation. According to him, this was so because, there is a lot of empty space in atoms. Hence the positive charged particles are also tiny like electrons.

### Hydrogen Spectra

If hydrogen gas is enclosed in a sealed tube and heat to high temperatures, it emits radiation. If this radiation is passed through a prsim, components are different wavelengths get deviated by different amounts and we get the hydrogen spectra on a screen. In the spectra of hydrogen atom, it is observed that light of wavelength 656.3 nm and then light of wave length 486.1 nm are present. Hydrogen atoms do not emit any radiation between 656.3 nm and 486.1 nm. Similarly radiation is observed at 434.1 nm and 4202.nm.

In the invisible region also, there is radiation emitted by the hydrogen atom at discrete wavelengths.

The wavelengths nicely fit the equation

1/λ = R [1/n² - 1/m²]

where R = 1.09737*10^7 m

n and m are integers with m>n.

The spectrum in the ultraviolet region is called Lyman series and you get the series by setting n = 1.

The hydrogen spectrum in the visible region is called Balmer series and you get the series by setting n = 2.

The hydrogen spectrum in infrared region is called Paschen series and you get the series by setting n= 3.

In the invisible region also, there is radiation emitted by the hydrogen atom at discrete wavelengths.

The wavelengths nicely fit the equation

1/λ = R [1/n² - 1/m²]

where R = 1.09737*10^7 m

^{-1}.n and m are integers with m>n.

The spectrum in the ultraviolet region is called Lyman series and you get the series by setting n = 1.

The hydrogen spectrum in the visible region is called Balmer series and you get the series by setting n = 2.

The hydrogen spectrum in infrared region is called Paschen series and you get the series by setting n= 3.

### Rutherford's Model

Rutherford experimented with alpha rays or particles. When he bombarded gold foils with alpha particles, Many went without deviation, some had some deviation and some were deflected by more than 90 and came back. Hence he made a conclusion that there was a particle with a mass equivalent to alpha particle inside the atom. The mass of an atom is concentrated in this particle.

The size of this particle was also estimated by Rutherford. Its linear size is 10 fermi ( 1 fermi is equal to 1 femtometre = 10^-15 m).

Rutherford proposed that the atom contains a positively charged tiny particle called nucleus. It contains the entire mass of the atom. Outside this nucleus, at some distance, electrons move around. The positive of charge of nucleus is exactly equal to the negative charge of the electrons of the atom.

Because electrons are very very light compared to the nucleus, due to heat only electrons come out.

Movement of electrons is to brought in and the coulomb force between the nucleus and the electron is assumed to provide only centripetal force to make the electron rotate in a circular motion.

The size of this particle was also estimated by Rutherford. Its linear size is 10 fermi ( 1 fermi is equal to 1 femtometre = 10^-15 m).

Rutherford proposed that the atom contains a positively charged tiny particle called nucleus. It contains the entire mass of the atom. Outside this nucleus, at some distance, electrons move around. The positive of charge of nucleus is exactly equal to the negative charge of the electrons of the atom.

Because electrons are very very light compared to the nucleus, due to heat only electrons come out.

Movement of electrons is to brought in and the coulomb force between the nucleus and the electron is assumed to provide only centripetal force to make the electron rotate in a circular motion.

### Difficulties with Rutherford’s Model

Rutherford’s model assumes that the electron rotates around the nucleus. Maxwell’s equations of a electromagnetism show that accelerated electron must continuously emit electromagnetic radiation. But a hydrogen does not emit radiation at ground level energy or normal energy. It emits radiation only when heated. Also, if it emits radiation it will lose energy and the radius of its circular motion will decreases and finally it will fall into the nucleus. Hence, the atomic model proposed by Rutherford needs modification. Bohr proposed such modifications.

### Bohr's Postulates and Model

1. The electrons revolve around the nucleus in circular orbits.

2. the orbit of the electron around the nucleus can be only some special values of radius. In these special radii orbits, the electron does not radiate energy as expected from Maxwell’s laws. These orbits are called stationary orbits.

3. The energy of the atom has a definite value when electrons are in a given stationary orbit. But the if more energy is provided to the atom, the electron can jump from one stationary orbit to another stationary orbit of higher energy. If it jumps from an orbit of higher energy (E2) to an orbit of lower energy (E1), it emits a photon of radiation. The energy of the emitted photon will be E2 – E1.

The wave length of the emitted radiation is given by the Einstein-Planck equation

E2-E1 = hυ = hc/λ

4. In stationary orbits, the angular momentum l of the electron about the nucleus is an in integral multiple of the Planck constant h divided by 2 π.

l = nh/2 π

This assumption is called Bohr’s quantization rule.

2. the orbit of the electron around the nucleus can be only some special values of radius. In these special radii orbits, the electron does not radiate energy as expected from Maxwell’s laws. These orbits are called stationary orbits.

3. The energy of the atom has a definite value when electrons are in a given stationary orbit. But the if more energy is provided to the atom, the electron can jump from one stationary orbit to another stationary orbit of higher energy. If it jumps from an orbit of higher energy (E2) to an orbit of lower energy (E1), it emits a photon of radiation. The energy of the emitted photon will be E2 – E1.

The wave length of the emitted radiation is given by the Einstein-Planck equation

E2-E1 = hυ = hc/λ

4. In stationary orbits, the angular momentum l of the electron about the nucleus is an in integral multiple of the Planck constant h divided by 2 π.

l = nh/2 π

This assumption is called Bohr’s quantization rule.

### Energy of an Hydrogen Atom

Assume that the nucleus has a positive charge Ze ( there are z protons each with positive charge e).

By equating the coulomb force acting between Ze and e to the centripetal acceleration mv²/r, we get r the radius at which the electron revolves.

r = Ze²/4π ε

From Bohr’s quantization rule,

mvr = nh/2 π

where n is a positive integer

Eliminating v from both the equations we get

r = ε

We get expression for v as

v = Ze²/2 ε

Hence allowed radii are proportinal to n² and for each value of n = 1,2,3…we allowed orbits.

The smallest radius orbit will have n = 1.

As we have expression for v, we can give an expression for kinetic energy when electron is in nth orbit is

K = ½ mv² = mZ²e

The potential energy of the atom is

V = - Ze²/4π ε

The expression for potential energy is obtained by assuming the potential energy to be zero when the nucleus and the electron are widely separated.

The total energy of the atom is

E = K+V = - mZ²e

When an atom is n

In giving an expression for the total energy of the atom, kinetic energy of the electron and potential energy of the electron-nucleus pair are considered. Kinetic energy of the nucleus is assumed to be negligible.

Bohr’s postulates can be used to find the allowed energies of the hydrogen atom when its single electron is in various stationary orbits. The methodology can be used any hydrogen like ions which have only one electron.. Therefore it is valid for He

By equating the coulomb force acting between Ze and e to the centripetal acceleration mv²/r, we get r the radius at which the electron revolves.

r = Ze²/4π ε

_{0}v²From Bohr’s quantization rule,

mvr = nh/2 π

where n is a positive integer

Eliminating v from both the equations we get

r = ε

_{0}h²n²/πmZe²We get expression for v as

v = Ze²/2 ε

_{0}hnHence allowed radii are proportinal to n² and for each value of n = 1,2,3…we allowed orbits.

The smallest radius orbit will have n = 1.

As we have expression for v, we can give an expression for kinetic energy when electron is in nth orbit is

K = ½ mv² = mZ²e

^{4}/8 ε_{0}²h²n²The potential energy of the atom is

V = - Ze²/4π ε

_{0}r = -mZ²e^{4}/4ε_{0}²h²n²The expression for potential energy is obtained by assuming the potential energy to be zero when the nucleus and the electron are widely separated.

The total energy of the atom is

E = K+V = - mZ²e

^{4}/8 ε_{0}²h²n²When an atom is n

^{th}stationary orbit, it is said to be in the n^{th}energy state.In giving an expression for the total energy of the atom, kinetic energy of the electron and potential energy of the electron-nucleus pair are considered. Kinetic energy of the nucleus is assumed to be negligible.

Bohr’s postulates can be used to find the allowed energies of the hydrogen atom when its single electron is in various stationary orbits. The methodology can be used any hydrogen like ions which have only one electron.. Therefore it is valid for He

^{+}, Li^{++}, Be^{+++}etc.### Radii of Different Orbit of Hydrogen Like Ion

r the radius at which the electron revolves.

r = Ze²/4π ε

For hydrogen, z =1 and we get r1 as 53 picometre ( 1pm = 10^-12 m) or 0.053 nm. This length is called the Bohr radius and is a convenient unit for measuring lengths in atomic physics. It is denoted by me as the symbol a

In terms of Bohr radius the second allowed radius is 4 a

r = Ze²/4π ε

_{0}v²For hydrogen, z =1 and we get r1 as 53 picometre ( 1pm = 10^-12 m) or 0.053 nm. This length is called the Bohr radius and is a convenient unit for measuring lengths in atomic physics. It is denoted by me as the symbol a

_{0}(In HC Verma a different symbol is given. I am using this symbol as a convenience).In terms of Bohr radius the second allowed radius is 4 a

_{0}and third is 9 a_{0}and so on. In general nth orbit of hydrogen atom is n²a_{0}.### Hydrogen Ion - Ground and Excited States

The state of an atom with the lowest energy is called its ground state.

The states with higher energies are called excited states.

Energy of hydrogen atom in the ground state is -13.6 eV.

Energy of hydrogen atom in the next excited state, that is n = 2 state is -3.4 eV.

The states with higher energies are called excited states.

Energy of hydrogen atom in the ground state is -13.6 eV.

Energy of hydrogen atom in the next excited state, that is n = 2 state is -3.4 eV.

### Hydrogen Spectra

When heated some atoms in the hydrogen become excited and when electrons jump from higher energy levels to lower energy levels in those excited atoms, photons with specific wavelengths are emitted or radiated.

If an electron jumps from mth orbit to nth orbit (m>n), the energy of the atom gets reduced from Em to En. The wavelength of the emitted radiation will be

1/ λ = (Em – En)/hc = RZ²{1/n² - 1/m²]

where R is the Rydberg constant.

R = 1.0973*10^7 m

In terms of the Rydberg constant total energy of the atom in the nth state is E = -RhcZ²/n²

For hydrogen atom, when n =1, E = -Rhc and we know its value is -13.6 eV.

Energy of 1 rydberg means -13.6 eV.

Rhc = 13.6eV

If an electron jumps from mth orbit to nth orbit (m>n), the energy of the atom gets reduced from Em to En. The wavelength of the emitted radiation will be

1/ λ = (Em – En)/hc = RZ²{1/n² - 1/m²]

where R is the Rydberg constant.

R = 1.0973*10^7 m

^{-}In terms of the Rydberg constant total energy of the atom in the nth state is E = -RhcZ²/n²

For hydrogen atom, when n =1, E = -Rhc and we know its value is -13.6 eV.

Energy of 1 rydberg means -13.6 eV.

Rhc = 13.6eV

### Hydrogen Spectra - Series Structure

Lyman series:

All transitions to n =1 state from higher state give the radiation in Lyman series.

Jumping of the electron from n =2 to n =1 gives

1/ λ = R[1 – 1/2²] = R(1 – ¼) which will give λ = 121.6 nm.

Jumping of the electron from n = ∞ to n = 1 gives

1/ λ = R[1 – 1/∞²] = R(1 -0) which gives λ = 91.2 nm.

Balmer seires

All transitions to n = 2 from higher states given radiations within the range of 656.3 nm and 365.0 nm. These wavelengths fall in the visible region.

Paschen series

The transitions or jumps to n = 3 from higher energy levels give Paschen series in the range 1875 nm to 822 nm.

All transitions to n =1 state from higher state give the radiation in Lyman series.

Jumping of the electron from n =2 to n =1 gives

1/ λ = R[1 – 1/2²] = R(1 – ¼) which will give λ = 121.6 nm.

Jumping of the electron from n = ∞ to n = 1 gives

1/ λ = R[1 – 1/∞²] = R(1 -0) which gives λ = 91.2 nm.

Balmer seires

All transitions to n = 2 from higher states given radiations within the range of 656.3 nm and 365.0 nm. These wavelengths fall in the visible region.

Paschen series

The transitions or jumps to n = 3 from higher energy levels give Paschen series in the range 1875 nm to 822 nm.

### Ionization Potential

The energy of the hydrogen atom in ground state is -13.6 eV. If we supply more than 13.6 eV to the hydrogen atom, the electron and the nucleus get separated and electron moves with some kinetic energy independently (Remember plasma in nuclear fusion).

The minimum energy needed to ionize an atom is called ionization energy. The potential difference through which an electron should be accelerated to acquire this much energy is called ionization potential.

Thus ionization energy of hydrogen atom in ground state is 13.6 eV and ionization potential is 13.6 V.

The minimum energy needed to ionize an atom is called ionization energy. The potential difference through which an electron should be accelerated to acquire this much energy is called ionization potential.

Thus ionization energy of hydrogen atom in ground state is 13.6 eV and ionization potential is 13.6 V.

### Binding Energy

Binding energy of a system is defined as the energy released when its constituents are brought from infinity to form the system. Now we know that binding energy of a hydrogen atom is 13.6 eV. The energy is zero when the electron and nucleus at infinite distance. When the electron is brought into n = 1 orbit, the energy becomes -13.6 eV and hence 13.6 eV is released which is the binding energy.

### Excitation potential

The energy needed to take the atom form its ground state to an excited state is called the excitation energy of that excited state.

As the hydrogen atom’s ground state energy is -13.6 eV and its energy when electron is in n =2 orbit is -3.4 eV, we have to supply 10.2 eV to excite a hydrogen atom to its first excited state which is electron in n = 2 orbit.

The potential through which an electron should be accelerated to acquire the excitation energy is the excitation potential.

The excitation potential needed bring hydrogen to its first excited state is 10.2 V.

As the hydrogen atom’s ground state energy is -13.6 eV and its energy when electron is in n =2 orbit is -3.4 eV, we have to supply 10.2 eV to excite a hydrogen atom to its first excited state which is electron in n = 2 orbit.

The potential through which an electron should be accelerated to acquire the excitation energy is the excitation potential.

The excitation potential needed bring hydrogen to its first excited state is 10.2 V.

### Limitations of Bohr Model

Maxwell’s theory of electromagnetism is not replaced or refuted in Bohr's model but it is arbitrarily assumed that in certain orbits, electrons get the licence to disobey the laws of electromagnetism and are allowed not to radiate energy.

### Quantum Mechanics of the Hydrogen Atom

Electron has a wave character as well as a particle character. The wave function of the electron ψ(r,t ) is obtained by solving Schrodinger’s wave equation. The probability of finding an electron is high where | ψ(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 ψ(r,t).

Quantum Mechanics of the Hydrogen Atom

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

-(h²/8π²m) [∂²ψ /∂x² + ∂²ψ /∂y² + ∂²ψ/∂z²] - Ze²ψ/4πε

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 ψ(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

Quantum Mechanics of the Hydrogen Atom

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

-(h²/8π²m) [∂²ψ /∂x² + ∂²ψ /∂y² + ∂²ψ/∂z²] - Ze²ψ/4πε

_{0}r = E ψwhere

(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 ψ(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 ε_{0}²h²n²## Sunday, November 9, 2008

### Production of X-rays

When highly energetic electrons are made to strike a metal target, electromagnetic radiation comes out. A large part of this radiation has wavelength of the order 0.1 nm (appx 1 A) and is known as X-ray.

### Continuous and Characteristic X-rays

If the X-rasy coming from a coolidge tube are examined for wavelengths present, and the intensity of different wavelengths are measurea and plotted, we can observe that there is a minimum wavelength below which no X-ray is emitted.

The wavelength below which no X-rays are emitted is called the cut-off wavelength or the threshold wavelength.

From the plot it can also be observed that at certain sharply defined wavelengths, the intensity of X-rays is very large. These X-rays are called characteristic X-rays.

At other wavelengths the intensity varies gradually and these X-rays are called continuous X-rays.

K X-Rays

X-rays emitted due to electronic transition from a higher energy state to a vacancy created in the K shell are called K X-rays.

The wavelength below which no X-rays are emitted is called the cut-off wavelength or the threshold wavelength.

From the plot it can also be observed that at certain sharply defined wavelengths, the intensity of X-rays is very large. These X-rays are called characteristic X-rays.

At other wavelengths the intensity varies gradually and these X-rays are called continuous X-rays.

K X-Rays

X-rays emitted due to electronic transition from a higher energy state to a vacancy created in the K shell are called K X-rays.

### Soft and Hard X-rays

The X-rays of low wave length are called hard X rays and X rays of large wave length are called soft X rays.

In terms of energy, harder means more energy in is each photon.

In terms of energy, harder means more energy in is each photon.

### Moseley's law

Square root of frequency of X rays = a(Z-b)

√(v) = a(Z-b)

where Z = position number of element.

a and b are constants

√(v) = a(Z-b)

where Z = position number of element.

a and b are constants

### Bragg’s law

2d sin θ = n λ

d = interplanar spacing of the crystal on which X-rays are incident

θ = is the incident angle at which X-rays are strongly reflected.

n = 1,2,3 …

λ = wave length of X-rays

Application of Bragg’s law:By using a monochromatic X-ray beam (having a single wave length) and noting the angles of strong reflection, the interplanar spacing d and several information about the structure of the solid can be obtained.

(Bragg Bday 2 July 1862)

Updated 23 Nov 2015, 9 Nov 2008

d = interplanar spacing of the crystal on which X-rays are incident

θ = is the incident angle at which X-rays are strongly reflected.

n = 1,2,3 …

λ = wave length of X-rays

Application of Bragg’s law:By using a monochromatic X-ray beam (having a single wave length) and noting the angles of strong reflection, the interplanar spacing d and several information about the structure of the solid can be obtained.

(Bragg Bday 2 July 1862)

Updated 23 Nov 2015, 9 Nov 2008

### Properties of X rays

X rays are electromagnetic waves of short wave lengths.

So they have many properties common with light.

1. They travel in straight lines in vacuum at a speed equal to that of light.

2. They are diffracted by crystals according to Bragg's law.

3. x-rays do not contain charged particles. hence they are not deflected by electric or magnetic field.

4. They effect a photographic plate. The effect is stronger than light.

Properties which are different than light

1. When incident on certain materials barium platinocyanide, X rays cause fluorescence.

2. When passed through a gas, X rays ionize the molecules of the gas.

So they have many properties common with light.

1. They travel in straight lines in vacuum at a speed equal to that of light.

2. They are diffracted by crystals according to Bragg's law.

3. x-rays do not contain charged particles. hence they are not deflected by electric or magnetic field.

4. They effect a photographic plate. The effect is stronger than light.

Properties which are different than light

1. When incident on certain materials barium platinocyanide, X rays cause fluorescence.

2. When passed through a gas, X rays ionize the molecules of the gas.

## Friday, November 7, 2008

### Atomic nucleus

Properties of Nucleus

A nucleus is made of protons and neutrons.

Studies have shown that average nucleus R of a nucleus may be written as

R = R0A^(1/3) .. (46.1)

where R0 = 1.1*10^-15 m ≈ 1.1 fm and A is the mass number

Density within a nucleus is independent of A.

A nucleus is made of protons and neutrons.

Studies have shown that average nucleus R of a nucleus may be written as

R = R0A^(1/3) .. (46.1)

where R0 = 1.1*10^-15 m ≈ 1.1 fm and A is the mass number

Density within a nucleus is independent of A.

### Nuclear Forces

When nucleons are kept at a separation of the order of femtometre (10^-15 m), a new kind of force, called nuclear force starts acting.

### Binding Energy

If the constituents of a hydrogen atom (a proton and an electron) are brought from infinity to form the atom, 13.6 3V of energy is released. Thus, the binding energy of a hydrogen atom in ground state is 13.6 eV. Also 13.6 eV energy must be supplied to the hydrogen atom in ground state to separate the constituents to large distances.

Similarly, the nucleons are bound together in a nucleus and energy must be supplied to the nucleus to separate the constituent nucleons to large distances. The amount of energy needed to do this is called the binding energy of the nucleus. If nucleons are brought together to form the nucleus from large separation this much energy is released.

It is evident from the above discussion that the rest mass energy of a nucleus is smaller than the rest mass energy of its constituents.

Similarly, the nucleons are bound together in a nucleus and energy must be supplied to the nucleus to separate the constituent nucleons to large distances. The amount of energy needed to do this is called the binding energy of the nucleus. If nucleons are brought together to form the nucleus from large separation this much energy is released.

It is evident from the above discussion that the rest mass energy of a nucleus is smaller than the rest mass energy of its constituents.

### Radioactive decay

Two main processes by which an unstable nucleus decays are alpha decay and beta decay.

Alpha decay

In alpha decay, the unstable nucleus emits an alpha particle reducing its proton number Z as well as its neutron number N by 2. As the proton number is changed, the element itself is changed and hence the chemical symbol of the residual nucleus is different from that of the original nucleus (Parent nucleus is original nucleus and the resulting nucleus due to decay is called daughter nucleus).

Alpha decay occurs in all nuclei with mass number A>210.

Beta Decay

Beta decay is a process in which either a neutron is converted into a proton or a proton is converted into a neutron.

When a neutron is converted into a proton, an electron and a new particle named antineutrino are created and emitted from the nucleus. The electron emitted from the nucleus is called a beta particle and is denoted by the symbol β-.

If the unstable nucleus has excess protons than needed for stability, a proton converts itself into a neutron. In the process, a positron and a neutrino are created and emitted from the nucleus.

Positron is represented by e+. The neutrino is represented by ν.

When a positron and electron collide, both the particles are destroyed and energy is made available.

The decay which gives beta rays consisting of positrons is called beta plus decay

Electron capture

A nucleus captures one of the atomic electrons, most likely an electron from the K shell, and a proton in the nucleus combines with the electron and converts itself into a neutron. A neutrino is created in process and emitted from the nucleus. So a combination of proton and electron results in neutron and neutrino.

Gamma Decay

When a daughter nucleus is formed due to alpha or beta decay, the nucleus may be at higher energy level compared to its ground or normal state. The electromagnetic radiation emitted in nuclear transitions from higher energy or excited state to ground state is called gamma ray.

Alpha decay

In alpha decay, the unstable nucleus emits an alpha particle reducing its proton number Z as well as its neutron number N by 2. As the proton number is changed, the element itself is changed and hence the chemical symbol of the residual nucleus is different from that of the original nucleus (Parent nucleus is original nucleus and the resulting nucleus due to decay is called daughter nucleus).

Alpha decay occurs in all nuclei with mass number A>210.

Beta Decay

Beta decay is a process in which either a neutron is converted into a proton or a proton is converted into a neutron.

When a neutron is converted into a proton, an electron and a new particle named antineutrino are created and emitted from the nucleus. The electron emitted from the nucleus is called a beta particle and is denoted by the symbol β-.

If the unstable nucleus has excess protons than needed for stability, a proton converts itself into a neutron. In the process, a positron and a neutrino are created and emitted from the nucleus.

Positron is represented by e+. The neutrino is represented by ν.

When a positron and electron collide, both the particles are destroyed and energy is made available.

The decay which gives beta rays consisting of positrons is called beta plus decay

Electron capture

A nucleus captures one of the atomic electrons, most likely an electron from the K shell, and a proton in the nucleus combines with the electron and converts itself into a neutron. A neutrino is created in process and emitted from the nucleus. So a combination of proton and electron results in neutron and neutrino.

Gamma Decay

When a daughter nucleus is formed due to alpha or beta decay, the nucleus may be at higher energy level compared to its ground or normal state. The electromagnetic radiation emitted in nuclear transitions from higher energy or excited state to ground state is called gamma ray.

### Law of Radioactive decay;

N = N0e- λ t

where

N = number of active nuclei at time t

N0 = number of active nuclei at t = 0.

λ = decay constant

-dN/dt = λN

-dN/dt gives the number of decays per unit time and is called the activity (A) of the sample

A = λN

A = A0e- λ t

where

N = number of active nuclei at time t

N0 = number of active nuclei at t = 0.

λ = decay constant

-dN/dt = λN

-dN/dt gives the number of decays per unit time and is called the activity (A) of the sample

A = λN

A = A0e- λ t

### Decay constant;

Law of radioactive decay

N = N0e- λ t

where

N = number of active nuclei at time t

N0 = number of active nuclei at t = 0.

λ = decay constant

N = N0e- λ t

where

N = number of active nuclei at time t

N0 = number of active nuclei at t = 0.

λ = decay constant

### Half-life and Mean life;

Half life:

The time elapased before half the active nuclei decay is called half-life and is denoted by t1/2.

t1/2. = 0.693/ λ

where

λ = decay constant.

Average life of the nuclei of a material

tav. = t1/2/0.693

The time elapased before half the active nuclei decay is called half-life and is denoted by t1/2.

t1/2. = 0.693/ λ

where

λ = decay constant.

Average life of the nuclei of a material

tav. = t1/2/0.693

### Properties and Uses of Nuclear Radiation

Properties and Uses of Nuclear Radiation

Alpha Ray

1. Each particle contains two protons and two neutrons. It is a helium nucleus.

2. It is made of positive particles and hence deflected by electric field as well as magnetic field.

3. Its penetrating power is low. Few cm in air also.

4. They travel at large speeds of the order of 10^6 m/s.

5. All particles from a source and decay scheme have the same energy.

6. Alpha rays produce scintillation (flashes of light) when they strike certain fluorescent materials such as barium platinocynide.

7. It causes ionization in gases.

Beta ray

1. It is a stream of electrons. Electrons are created during nuclear transformation.

2. They are negative particles and hence deflected by electric as well as magnetic fields.

3. Penetrating power greater than alpha rays. They can travel several meters in air before its intensity drops down to small values.

4. Ionizing power is less than alpha rays.

5. beta rays also produced scintillation but it is weak.

6. The energy of particles is not uniform as they share energy with antineutrinos. Energy of beta particles varies from zero to a maximum

Beta plus ray

It has all the properties of beta rays or beta negative rays, except that it is made of positively charged particles.

Gamma Ray

1. Gamma ray is an electromagnetic radiation of short wavelength. Its wavelength is shorted than X-rays.

2. Many properties are similar to X-rays.

3. As there is no charge no deflection in electric or magnetic fields.

4. All the photons coming from a particular gamma decay scheme has the same energy.

5. As it is electromagnetic wave, gamma ray travels with the velocity ‘c’ in vacuum.

Alpha Ray

1. Each particle contains two protons and two neutrons. It is a helium nucleus.

2. It is made of positive particles and hence deflected by electric field as well as magnetic field.

3. Its penetrating power is low. Few cm in air also.

4. They travel at large speeds of the order of 10^6 m/s.

5. All particles from a source and decay scheme have the same energy.

6. Alpha rays produce scintillation (flashes of light) when they strike certain fluorescent materials such as barium platinocynide.

7. It causes ionization in gases.

Beta ray

1. It is a stream of electrons. Electrons are created during nuclear transformation.

2. They are negative particles and hence deflected by electric as well as magnetic fields.

3. Penetrating power greater than alpha rays. They can travel several meters in air before its intensity drops down to small values.

4. Ionizing power is less than alpha rays.

5. beta rays also produced scintillation but it is weak.

6. The energy of particles is not uniform as they share energy with antineutrinos. Energy of beta particles varies from zero to a maximum

Beta plus ray

It has all the properties of beta rays or beta negative rays, except that it is made of positively charged particles.

Gamma Ray

1. Gamma ray is an electromagnetic radiation of short wavelength. Its wavelength is shorted than X-rays.

2. Many properties are similar to X-rays.

3. As there is no charge no deflection in electric or magnetic fields.

4. All the photons coming from a particular gamma decay scheme has the same energy.

5. As it is electromagnetic wave, gamma ray travels with the velocity ‘c’ in vacuum.

### Binding energy and its calculation

Energy from the Nucleus

Nuclear energy may be obtained either by breaking a heavy nucleus into two nuclei of middle weight (fission) or by combining two light nuclei to form a middle weight nucleus (fusion).

Reason: The middle weight nuclei are more tightly bound than heavy weight nuclei. When the nucleons of a heavy nucleus regroup in two middle weight nuclei called fragments the total binding energy increases and the rest mass energy decreases. The difference in energy appears as the kinetic energy of the fragments or in some other form.

In the case of fusion, the light weight nuclei are less tightly bound than the middle weight nuclei. Therefore, if two light weight nuclei combine, the binding energy increases and the rest mass decreases. Energy is released in the form of kinetic energy or in some other external form.

Nuclear energy may be obtained either by breaking a heavy nucleus into two nuclei of middle weight (fission) or by combining two light nuclei to form a middle weight nucleus (fusion).

Reason: The middle weight nuclei are more tightly bound than heavy weight nuclei. When the nucleons of a heavy nucleus regroup in two middle weight nuclei called fragments the total binding energy increases and the rest mass energy decreases. The difference in energy appears as the kinetic energy of the fragments or in some other form.

In the case of fusion, the light weight nuclei are less tightly bound than the middle weight nuclei. Therefore, if two light weight nuclei combine, the binding energy increases and the rest mass decreases. Energy is released in the form of kinetic energy or in some other external form.

### Nuclear Fission

The rest mass energy of the heavy nucleus represented by E1 is greater than the rest mass energy of the fragments represented by E3. But the energy level of the heavy nucleus is to be increased to E2 to get the fission process started according to classical physics.

But according to quantum mechanics, fission can take place even if no external energy is given. Such a fission process is termed as barrier penetration. The amount of energy created and the time for which it is created through a barrier penetration process are related through Heisenberg uncertainty relation.

∆E. ∆t ≈ h/2 π

Where h is the Planck constant

Barrier penetration is possible but is not easy.

But according to quantum mechanics, fission can take place even if no external energy is given. Such a fission process is termed as barrier penetration. The amount of energy created and the time for which it is created through a barrier penetration process are related through Heisenberg uncertainty relation.

∆E. ∆t ≈ h/2 π

Where h is the Planck constant

Barrier penetration is possible but is not easy.

### Uranium Fission Reactor

Breeder Reactors

92238U can capture neutrons and become

92239U. On B radiation it becomes

93239Np. On beta radiation it becomes

94239Pu.

94239Pu when hit by neutron becomes 94240Pu, which is a fissionable material. Thus if out of the 2.47 neutrons produced on average in fission reaction, one neutron is absorbed by 238U we produce fuel equivalent to what is consumed. Such a reactor is called breeder reactor.

92238U can capture neutrons and become

92239U. On B radiation it becomes

93239Np. On beta radiation it becomes

94239Pu.

94239Pu when hit by neutron becomes 94240Pu, which is a fissionable material. Thus if out of the 2.47 neutrons produced on average in fission reaction, one neutron is absorbed by 238U we produce fuel equivalent to what is consumed. Such a reactor is called breeder reactor.

### Nuclear Fusion

For he light nuclei to come together with in a distance of 1 fm (femtometer), we need a temperature of the order of 10^9 K. At that temperature electrons are completely detached from atoms and only nuclei remain. It is called plasma. In Sun, the temperature is 1.5*10^7 K and fusion is taking place. So fusion can take place due to barrier penetration process at 10^7 K.

### Fusion in Laboratory

The major problem on earth for fusion reaction is holding plasma at high temperature for extended period of time.

Lawson criterion for fusion reactor

In order to get an energy output greater than the energy input, a fusion reactor should achieve

n τ >10^14 s/cm³

where

n = the density of the interacting particles

τ = confinement time

The quantity n τ in s/cm³ is called Lawson number

Tokamak Design

In this design, the deuterium plasma is contained in a toroidal region by specially designed magnetic field. The directions and magnitudes of the magnetic field are so managed in the toroidal space that whenever a charge plasma particle attempts to go out q

With such designs, confinement of the plasma has been achieved for short duration of few microseconds.

A large fusion machine known as Joint European Torus (JET) is designed to achieve fusion energy on this principle.

At the Institute of Plasma Research (IPR) Ahmedabad, a small machine named Aditya is functioning on the Tokamak design. This machine is being used to study properties of plasma.

Inertial Confinement

It is an alternate method of confinement of plasma. A small solid pellet is made that contains deuterium and tritium. Intense laser beams are directed on the pellet from many directions on all the sides. The laser vaporizes the pellet converting it into plasma and then compresses it. The density increases by 10^3 to 10^4 time the initial density and temperature raises to high values. Fusion occurs in these conditions. In this method also so far, confinement for very small duration is only achieved.

The source of fuel for fusion is water only and water is abundant in oceans. Also these reactions do not result in radioactive emissions like that of fission.

Lawson criterion for fusion reactor

In order to get an energy output greater than the energy input, a fusion reactor should achieve

n τ >10^14 s/cm³

where

n = the density of the interacting particles

τ = confinement time

The quantity n τ in s/cm³ is called Lawson number

Tokamak Design

In this design, the deuterium plasma is contained in a toroidal region by specially designed magnetic field. The directions and magnitudes of the magnetic field are so managed in the toroidal space that whenever a charge plasma particle attempts to go out q

**v**×**B**force tends to push it back into the toroidal volume.With such designs, confinement of the plasma has been achieved for short duration of few microseconds.

A large fusion machine known as Joint European Torus (JET) is designed to achieve fusion energy on this principle.

At the Institute of Plasma Research (IPR) Ahmedabad, a small machine named Aditya is functioning on the Tokamak design. This machine is being used to study properties of plasma.

Inertial Confinement

It is an alternate method of confinement of plasma. A small solid pellet is made that contains deuterium and tritium. Intense laser beams are directed on the pellet from many directions on all the sides. The laser vaporizes the pellet converting it into plasma and then compresses it. The density increases by 10^3 to 10^4 time the initial density and temperature raises to high values. Fusion occurs in these conditions. In this method also so far, confinement for very small duration is only achieved.

The source of fuel for fusion is water only and water is abundant in oceans. Also these reactions do not result in radioactive emissions like that of fission.

### 46. Nucleus - Revision Facilitator

Recollect points under the topic

If required

46.1 Atomic nucleus;

46.2 Nuclear Forces

46.3 Binding Energy

46.4 Radioactive decay

46.5 Law of Radioactive decay;

Decay constant

Half-life and Mean life

46.6 Properties and Uses of Nuclear Radiation

46.7 Energy from the Nucleus

46.8 Nuclear Fission

46.9 Uranium Fission Reactor

46.10 Nuclear Fusion

46.11 Fusion in Laboratory

http://iit-jee-physics.blogspot.com/2008/03/concept-review-ch46-nucleus.html

If required

**right click**on the topic if link is provided, read the material, close it and come back.46.1 Atomic nucleus;

46.2 Nuclear Forces

46.3 Binding Energy

46.4 Radioactive decay

46.5 Law of Radioactive decay;

Decay constant

Half-life and Mean life

46.6 Properties and Uses of Nuclear Radiation

46.7 Energy from the Nucleus

46.8 Nuclear Fission

46.9 Uranium Fission Reactor

46.10 Nuclear Fusion

46.11 Fusion in Laboratory

http://iit-jee-physics.blogspot.com/2008/03/concept-review-ch46-nucleus.html

### 1. Introduction to Physics - Revision Facilitator

Sections

1. Introduction to physics

1.1 What is Physics

1.2 Physics and Mathematics

1.3 Units

1.4 Definitions of base units

1.5 Dimension

1.6 Uses of dimension

1.7 Order of magnitude

1.8 The structure of world

1. Introduction to physics

1.1 What is Physics

1.2 Physics and Mathematics

1.3 Units

1.4 Definitions of base units

1.5 Dimension

1.6 Uses of dimension

1.7 Order of magnitude

1.8 The structure of world

### 2. Physics and Mathematics - Revision Facilitator

2. Physics and mathematics

Sections

2.1 Vectors and scalars

2.2 Equality of vectors

2.3 Addition of vectors

2.4 Multiplication of a vector by a number

2.5 Subtraction of vectors

2.6 Resolution of vectors

2.7 DCT product or scalar product of two vectors

2.8 Cross product or vector product of two vectors

2.9 Differential calculus: dy/dx as rate measure

2.10 Maxima and Minima

2.11 Integral calculus

2.12 Significant digits

2.13 Significant digits in calculations

2.14 Errors in measurements

Sections

2.1 Vectors and scalars

2.2 Equality of vectors

2.3 Addition of vectors

2.4 Multiplication of a vector by a number

2.5 Subtraction of vectors

2.6 Resolution of vectors

2.7 DCT product or scalar product of two vectors

2.8 Cross product or vector product of two vectors

2.9 Differential calculus: dy/dx as rate measure

2.10 Maxima and Minima

2.11 Integral calculus

2.12 Significant digits

2.13 Significant digits in calculations

2.14 Errors in measurements

### 3. Rest and Motion: Kinematics - Revision Facilitator

3. Rest and Motion: Kinematics

Sections

3.1 Rest and Motion

3.2 Distance and displacement

3.3 average speed and instantaneous speed

3.4 Average velocity and instantaneous velocity

3.5 Average acceleration and instantaneous acceleration

3.6 Motion in a straight line

3.7 Motion in a plane

3.8 Projectile motion

3.9 Change of frame

Displacement – 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

Sections

3.1 Rest and Motion

3.2 Distance and displacement

3.3 average speed and instantaneous speed

3.4 Average velocity and instantaneous velocity

3.5 Average acceleration and instantaneous acceleration

3.6 Motion in a straight line

3.7 Motion in a plane

3.8 Projectile motion

3.9 Change of frame

**Mind Map****Rest - Motion – displacement – Speed – Velocity – Acceleration – Frame of Reference**Displacement – 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 - Revision Facilitator

4. The forces

Sections

4.1 Introduction

4.2 Gravitational forces

4.3 Electromagnetic (EM) forces

4.4 Nuclear Forces

4.5 Weak forces

4.6 Scope of Classical physics

Mind Map

Sections

4.1 Introduction

4.2 Gravitational forces

4.3 Electromagnetic (EM) forces

4.4 Nuclear Forces

4.5 Weak forces

4.6 Scope of Classical physics

Mind Map

**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.### 26. Laws of Thermodynamics - Revision Facilitator

Recollect some points for each topic.

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26.1 The first law of thermodynamics

26.2 Work done by a gas

26.3 Heat engines

26.4 The second law of thermodynamics

26.5 Reversible and irrerversible processes

26.6 entropy

27.7 Carnot engine

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26.1 The first law of thermodynamics

26.2 Work done by a gas

26.3 Heat engines

26.4 The second law of thermodynamics

26.5 Reversible and irrerversible processes

26.6 entropy

27.7 Carnot engine

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### 29. Electric Field and Potential - Revision Facilitator

Recollect some points for each topic.

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29.1 What is electric charge?

29.2 Coulomb's law

29.3 electric field

29.4 Lines of electric force

29.5 Electric potential energy

29.6 Electric potential

29.7 Electric potential due to a point charge

29.8 Relation between electric field and potential

29.9 Electric dipole

29.10 Torque on an electric dipole placed in an lectric field

29.11 Potential energy of a diple placed in a uniform electric field

29.12 Conductors, insulators nad semiconductors

29.13 The electric field inside a conductor

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29.1 What is electric charge?

29.2 Coulomb's law

29.3 electric field

29.4 Lines of electric force

29.5 Electric potential energy

29.6 Electric potential

29.7 Electric potential due to a point charge

29.8 Relation between electric field and potential

29.9 Electric dipole

29.10 Torque on an electric dipole placed in an lectric field

29.11 Potential energy of a diple placed in a uniform electric field

29.12 Conductors, insulators nad semiconductors

29.13 The electric field inside a conductor

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### 30. Gauss's Law - Revision Facilitator

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30.1 Flux of electric field through a surface

30.2 Solid angle

30.3 Gauss’s law and its derivation from Couloms’s law

30.4 Gauss's law's application

30.5.Spherical charge distributions

30.6 Earthing a conductor

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30.1 Flux of electric field through a surface

30.2 Solid angle

30.3 Gauss’s law and its derivation from Couloms’s law

30.4 Gauss's law's application

30.5.Spherical charge distributions

30.6 Earthing a conductor

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Concept review of the full chapter

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## Thursday, November 6, 2008

### 31. Capacitors - Revision Facilitator

Recollect some points for each topic and right click on the link to open it in a new window, read it, close it and come back here.

31.1 Capacitance;

31.2 Calculation of capacitance

31.3 Capacitors in series and parallel;

31.4 Parallel plate capacitor

31.5 Energy stored in a capacitor.

31.6 Dielectrics

31.7 Parallel plate capacitor with dielectrics;

31.8 An alternative form of Gauss's law

31.9 Electric field due to a point charge q placed in a an infinite dielectric

31.10 Energy in the Electric field in a dielectric

31.11 Corona discharge

31.12 High voltage generator

Links will be created in due course.

31.1 Capacitance;

31.2 Calculation of capacitance

31.3 Capacitors in series and parallel;

31.4 Parallel plate capacitor

31.5 Energy stored in a capacitor.

31.6 Dielectrics

31.7 Parallel plate capacitor with dielectrics;

31.8 An alternative form of Gauss's law

31.9 Electric field due to a point charge q placed in a an infinite dielectric

31.10 Energy in the Electric field in a dielectric

31.11 Corona discharge

31.12 High voltage generator

Links will be created in due course.

### 32. Electric Current in Conductors - Revision Facilitator

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32.1 Electric current and current density

32.2 Drift speed

32.3 Ohm's law

32.4 Temperature dependence of resistivity

32.5 Battery and EMF

32.6 Energy transfer in an electric current

32.7 Kirchhoff's Laws

32.8 Combination of resistors in series and parallel

32.9 Grouping of batteries

32.10 Wheatstone bridge

32.11 Ammeter and Voltmeter

32.12 Stretched wire potentiometer

32.13 Chargin and discharging of capactiros

32.14 Atmospheric electricity

Links will be created in due course.

32.1 Electric current and current density

32.2 Drift speed

32.3 Ohm's law

32.4 Temperature dependence of resistivity

32.5 Battery and EMF

32.6 Energy transfer in an electric current

32.7 Kirchhoff's Laws

32.8 Combination of resistors in series and parallel

32.9 Grouping of batteries

32.10 Wheatstone bridge

32.11 Ammeter and Voltmeter

32.12 Stretched wire potentiometer

32.13 Chargin and discharging of capactiros

32.14 Atmospheric electricity

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### 33. Thermal and Chemical Effects of Electric Current - Revision Facilitator

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33.1 Joule's law of heating

33.2 Verification of Joule's Laws

33.3 Seebeck effect

33.4 Peltier effect

33.5 Thomson effect

33.6 Explanation Seebeck, Peltier, Thomson effects

33.7 Electrolysis

33.8 Faraday's Laws of electrolysis

33.9 Voltameter or Coulomb meter

33.10 Primary and Secondary cells

33.11 Primary cells

33.12 Secondry Cell: Lead accumulator

Links will be created in due course.

33.1 Joule's law of heating

33.2 Verification of Joule's Laws

33.3 Seebeck effect

33.4 Peltier effect

33.5 Thomson effect

33.6 Explanation Seebeck, Peltier, Thomson effects

33.7 Electrolysis

33.8 Faraday's Laws of electrolysis

33.9 Voltameter or Coulomb meter

33.10 Primary and Secondary cells

33.11 Primary cells

33.12 Secondry Cell: Lead accumulator

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### 34. Magnetic Field - Revision Facilitator

Recollect some points for each topic and right click on the link to open it in a new window, read it, close it and come back here.

1. Introduction

2. Definition of Magnetic field

3. Relation between electric and magentic fields

4. Motion of a charged aprticle in a uniform magentic field

5. Magnetic force on a current carrying wire

6. Torque on a current loop.

Links will be created in due course.

1. Introduction

2. Definition of Magnetic field

3. Relation between electric and magentic fields

4. Motion of a charged aprticle in a uniform magentic field

5. Magnetic force on a current carrying wire

6. Torque on a current loop.

Links will be created in due course.

### 35. Magnetic Field Due to a Current - Revision Facilitator

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35.1 Bio Savart Law

35.2 Magnetic field due to current in a straight wire

35.3 Force between parallel currents

35.4 Field due to a circular current

35.5 Ampere's law

35.6 Magnetic field at a point due to a long straight current

35.7 Solenoid

Links will be created in due course.

35.1 Bio Savart Law

35.2 Magnetic field due to current in a straight wire

35.3 Force between parallel currents

35.4 Field due to a circular current

35.5 Ampere's law

35.6 Magnetic field at a point due to a long straight current

35.7 Solenoid

Links will be created in due course.

## Wednesday, November 5, 2008

### 38. Electro Magnetic Induction - Revision Facilitator

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38.1 Faraday's law,

38.2 Lenz's law;

38.3 The origin of induced emf

38.4 Eddy Current

38.5 Self and mutual inductance;

38.6 RC, LR and LC circuits with d.c. and a.c. sources.

38.7 Energy stored in an inductor

38.8 mutual inductance;

38.9 Induction coil

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38.1 Faraday's law,

38.2 Lenz's law;

38.3 The origin of induced emf

38.4 Eddy Current

38.5 Self and mutual inductance;

38.6 RC, LR and LC circuits with d.c. and a.c. sources.

38.7 Energy stored in an inductor

38.8 mutual inductance;

38.9 Induction coil

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### Ch.43 Bohr's Model and Physics of the Atom

43.1 Early atomic models

43.2 Hydrogen Spectra

43.3 Difficulties in Rutherford Model

43.4 Bohr's model

43.5 Limitations of Bohr's Model

43.6 The wave Function of an Electron

43.7 Quantum Mechanics of the Hydrogen Atom

43.8 Nomencluature in Atomic Physics

43.9 Laser

43.2 Hydrogen Spectra

43.3 Difficulties in Rutherford Model

43.4 Bohr's model

43.5 Limitations of Bohr's Model

43.6 The wave Function of an Electron

43.7 Quantum Mechanics of the Hydrogen Atom

43.8 Nomencluature in Atomic Physics

43.9 Laser

### 44. X-Rays - Revision Facilitator

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Production of X-rays

Continuous and Characteristic X-rays

Soft and Hard X-rays

Moseley's law

Bragg’s law

Properties of X rays

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Production of X-rays

Continuous and Characteristic X-rays

Soft and Hard X-rays

Moseley's law

Bragg’s law

Properties of X rays

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### JEE Physics Revision Facilitator - All Chapters Combined

Have a quick review to recollect the material for each section.

1. Introduction to physics

1.1 What is Physics

1.2 Physics and Mathematics

1.3 Units

1.4 Definitions of base units

1.5 Dimension

1.6 Uses of dimension

1.7 Order of magnitude

1.8 The structure of world

2. Physics and mathematics

2.1 Vectors and scalars

2.2 Equality of vectors

2.3 Addition of vectors

2.4 Multiplication of a vector by a number

2.5 Subtraction of vectors

2.6 Resolution of vectors

2.7 DCT product or scalar product of two vectors

2.8 Cross product or vector product of two vectors

2.9 Differential calculus: dy/dx as rate measure

2.10 Maxima and Minima

2.11 Integral calculus

2.12 Significant digits

2.13 Significant digits in calculations

2.14 Errors in measurements

3. Rest and Motion: Kinematics

3.1 Rest and Motion

3.2 Distance and displacement

3.3 average speed and instantaneous speed

3.4 Average velocity and instantaneous velocity

3.5 Average accleration and instantaneous aceleration

3.6 Motion in a straight line

3.7 Motion in a plane

3.8 Projectile motion

3.9 Change of frame

4. The forces

4.1 Introduction

4.2 Gravitational forces

4.3 Electromagnetic (EM) forces

4.4 Nuclear Forces

4.5 Weak forces

4.6 Scope of Classical physics

5. Newtons laws of motion

5.1 Newton's First law

5.2 Newton's second law

5.3 Working with Newton's laws

5.4 Newton's third law of motion

5.5 Pseudo forces

5.6 The Horse and the cart

5.7 Inertia

6. Friction

6.1 Friction as the component of contact force

6.2 Kinetic friction

6.3 Static friction

6.4 Laws of friction

6.5 Understanding friction at atomic level

6.6 A Laboratory method to measure

7. Circular motion

7.1 Angular variables

7.2 Unit vectors along the radius and the tangent

7.3 Acceleration in circular motion

7.4 Dynamics of circular motion

7.5 Circular turnings and banking of roads

7.6 Centrifugal force

7.7 Effect of earth's rotation on apprarent weight

8. Work and energy

1. Kinetic enery

2. Work and work energy theorem

3. Calculation of work done

4. Work energy theorem for a system of particles

5. Potential energy

6. Conservative and nonconservative forces

7. Definition of Potential energy and conservation of mechanical energy

8. Change in the potential energy in a rigid body motion

9. Gravitational potential energy

10. Potential energy oif a compressed or extended spring

11. Different forms of energy: Mass energy equivalence

9. Centre of mass,linear momentum,collision

1. Centre of mass

2. Centre of mass of continuous bodies

3. Motion of the Centre of mass

4. Linear momentum and its conservation principle

5. Rocket propulsion

6. Collision

7. Elastic collision in one dimension

8. Perfectly inelastic collision in one dimension

9. Coefficient of restitution

10. Elastic collision in two dimensions

11. Impulse and impulsive force

10. Rotational mechanics

1. Rotation of a rigid body

2. Kinematics

3. Rotational dynamics

4. Torque of a force about the axis of rotation

5. Г = Iα

6. Bodies in equilibrium

7. Bending of a cyclist on a horizontal turn

8. Angular momentum

9. L = Iα

10. Conservation of angular momentum

11. Angular impulse

12. Kinetic energy of a rigid body rotating about a given axis

13. Power delivered and work done by a torque

14. Calculation of moment of inertia

15. Two important theorems on moment of inertia

16. Combined rotation and translation

17. Rolling

18. Kinetic energy of a body in combined rotation and translation

19. Angular momentum of a body in combined rotation and translation

20. Why does a rolling sphere slow down

1. Introduction to physics

1.1 What is Physics

1.2 Physics and Mathematics

1.3 Units

1.4 Definitions of base units

1.5 Dimension

1.6 Uses of dimension

1.7 Order of magnitude

1.8 The structure of world

2. Physics and mathematics

2.1 Vectors and scalars

2.2 Equality of vectors

2.3 Addition of vectors

2.4 Multiplication of a vector by a number

2.5 Subtraction of vectors

2.6 Resolution of vectors

2.7 DCT product or scalar product of two vectors

2.8 Cross product or vector product of two vectors

2.9 Differential calculus: dy/dx as rate measure

2.10 Maxima and Minima

2.11 Integral calculus

2.12 Significant digits

2.13 Significant digits in calculations

2.14 Errors in measurements

3. Rest and Motion: Kinematics

3.1 Rest and Motion

3.2 Distance and displacement

3.3 average speed and instantaneous speed

3.4 Average velocity and instantaneous velocity

3.5 Average accleration and instantaneous aceleration

3.6 Motion in a straight line

3.7 Motion in a plane

3.8 Projectile motion

3.9 Change of frame

4. The forces

4.1 Introduction

4.2 Gravitational forces

4.3 Electromagnetic (EM) forces

4.4 Nuclear Forces

4.5 Weak forces

4.6 Scope of Classical physics

5. Newtons laws of motion

5.1 Newton's First law

5.2 Newton's second law

5.3 Working with Newton's laws

5.4 Newton's third law of motion

5.5 Pseudo forces

5.6 The Horse and the cart

5.7 Inertia

6. Friction

6.1 Friction as the component of contact force

6.2 Kinetic friction

6.3 Static friction

6.4 Laws of friction

6.5 Understanding friction at atomic level

6.6 A Laboratory method to measure

7. Circular motion

7.1 Angular variables

7.2 Unit vectors along the radius and the tangent

7.3 Acceleration in circular motion

7.4 Dynamics of circular motion

7.5 Circular turnings and banking of roads

7.6 Centrifugal force

7.7 Effect of earth's rotation on apprarent weight

8. Work and energy

1. Kinetic enery

2. Work and work energy theorem

3. Calculation of work done

4. Work energy theorem for a system of particles

5. Potential energy

6. Conservative and nonconservative forces

7. Definition of Potential energy and conservation of mechanical energy

8. Change in the potential energy in a rigid body motion

9. Gravitational potential energy

10. Potential energy oif a compressed or extended spring

11. Different forms of energy: Mass energy equivalence

9. Centre of mass,linear momentum,collision

1. Centre of mass

2. Centre of mass of continuous bodies

3. Motion of the Centre of mass

4. Linear momentum and its conservation principle

5. Rocket propulsion

6. Collision

7. Elastic collision in one dimension

8. Perfectly inelastic collision in one dimension

9. Coefficient of restitution

10. Elastic collision in two dimensions

11. Impulse and impulsive force

10. Rotational mechanics

1. Rotation of a rigid body

2. Kinematics

3. Rotational dynamics

4. Torque of a force about the axis of rotation

5. Г = Iα

6. Bodies in equilibrium

7. Bending of a cyclist on a horizontal turn

8. Angular momentum

9. L = Iα

10. Conservation of angular momentum

11. Angular impulse

12. Kinetic energy of a rigid body rotating about a given axis

13. Power delivered and work done by a torque

14. Calculation of moment of inertia

15. Two important theorems on moment of inertia

16. Combined rotation and translation

17. Rolling

18. Kinetic energy of a body in combined rotation and translation

19. Angular momentum of a body in combined rotation and translation

20. Why does a rolling sphere slow down

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