Modern Physics lesson 1 (Black body Radiation) theory

Question 1

after the discovery of phenomenon of what did they prove that light is a electromagnetic wave

Answer 1

interference, diffraction, polarization

Question 1

it was assumed that light consists of tiny minute particles called

Answer 1

corpuscles

Question 2

tell me about the emission and absorption of energy

Answer 2

emission and absorption of energy is not continuous, but discrete.

Question 2

what are matter waves

Answer 2

A particle in motion is associated with waves called matter waves.

Question 2

when is the object perfectly black XD

Answer 2

A perfect black body is the one which absorbs the entire radiations incident on
it, it neither reflects nor transmits radiations, and hence it appears perfectly
black

Question 3

what happens when you heat a black body

Answer 3

it radiates all kind of wavelengths

Question 4

The black body radiation is characteristic of its

Answer 4

temperature

Question 5

What are radiation curves?

Answer 5

when a graph of energy density is plotted against wavelength, curves are obtained as
shown in the figure.

Question 5

What are following conclusions can be drawn from the radiation curves.

Answer 5

1) The energy is not uniformly distributed in the spectrum of black body
radiation.
2) At a given temperature, energy density increases with wave length,
becomes maximum for a particular wavelength and then decreases as
wavelength increases.
3) As temperature increases, intense radiation represented by peak of the
curve shifts towards shorter wavelength region.

Question 6

How many Laws of black body radiation are there

Answer 6

Stefan’s law of Radiation
Wein’s law of energy distribution
jean’s law of energy distribution
Planck’s law of radiation

Question 6

What is Stefan’s law of radiation?

Answer 6

The Stefan’s law states that energy radiated per second per unit area is directly proportional to the fourth power of absolute temperature…..E directly proportional T 4, or E = σ T^4

Question 7

What is Wien’s law of radiation?

Answer 7

Wien assumed that black body radiation in a cavity is supposed to be emitted by resonators of molecular dimensions having
Maxwellian velocity distribution and applied law of kinetic theory of gases to
obtain formula for energy distribution
Uλdλ=C1λ^-5e^[-(C2/λT)dλ

Question 7

Drawbacks of Wien’s Law

Answer 7

This law explains the energy distribution only in shorter wavelengths & fails to
explain the energy distribution in longer wavelength region
when temperature is zero, energy density is finite. This is a contradiction to Stefan’s law

Question 7

What is Lord Rayleigh –Jeans law of Radiation

Answer 7

Lord Rayleigh–Jeans considered the black body radiations full of electromagnetic
waves of all wavelengths, between 0 and infinity, which due to reflection, form
standing waves.
They calculated number of possible waves having wavelengths
between λand λ+dλ and by using law of equi-partition of energy, they established
distribution law as: Uλdλ=8πkT^-4dλ
Because of the presence of the factor t-4 in the equation, the energy radiated by the black body should rapidly decrease with
increasing wavelength.

Question 8

Drawbacks of Rayleigh–Jeans law

Answer 8

Lord Rayleigh–Jeans law holds good only for longer wavelengths region and fails to explain energy distribution in shorter wavelength region,
The failure of the Rayleigh–Jeans law to explain the aspect of very little emission of radiation beyond the violet region towards the lower wavelength side of the spectrum is particularly referred to as Ultra-violet
Catastrophe.

Question 8

Planck’s Law of Radiation

Answer 8

1) The black body radiations in a cavity are composed of tiny oscillators having molecular dimensions, which can vibrate with all possible frequencies.
2) The frequency of radiations emitted by oscillators is same as the frequency of its vibrations.
3) An oscillator cannot emit energy in a continuous manner, but emission
and absorption can take place only in terms of small packet of energy called Quanta, the oscillator can have only discrete energy values E given by nh ν

Question 9

explain Compton scattering and Compton Effect.

Answer 9

Compton discovered that when monochromatic beam of very
high frequency radiation such as X-rays or Gamma rays is made to scatter
through a substance
the scattered radiation found to contain two components one having same frequency or wavelength as that of incident radiation, known as unmodified radiation
the other, having lower frequency or longer
wavelength than incident radiation known as modified radiation. This is called
Compton scattering
during the process an electron recoils with certain velocity. This phenomenon is called Compton Effect.

Question 10

What is modified radiation

Answer 10

the scattered radiation having lower frequency or longer wavelength than incident radiation known as modified radiation

Question 11

What is unmodified radiation

Answer 11

the scattered radiation one having same frequency or wavelength as that of incident radiation, known as unmodified radiation

Question 11

What is Quanta or photons

Answer 11

radiation is composed of small packets of energy called Quanta or photons having energy hv

Question 11

explain how the change in wavelength takes place during Compton effect

Answer 11

*According to Compton, when a
photon of energy hv of momentum h/λ moving with velocity equal to velocity of
light, obeying laws of conservation of energy and momentum, strikes an
electron which is at rest, there occurs an elastic collision between two particles
namely photon and electron
*When photon of energy h strikes the electron at rest, photon transfers some of
its energy to electron, therefore photon loses its energy, hence, its frequency
reduces to v1 and wavelength changes to λ1
* the scattered photon makes an
angle phi with the incident direction, during the process an electron gains kinetic
energy and recoils with certain velocity.
*by applying laws of conservation of energy and momentum we get
λ’-λ=h(1-cosphi)/m0c…..mo = mass of electron at rest

Question 11

the change in wavelength (Compton shift) depends on?

Answer 11

thechange in wavelength (Compton shift) depends neither on the incident
wavelength nor the scattering material, but depends only on the angle of scattering

Question 12

What is Compton shift.

Answer 12

The change in wavelength λ’-λ is called Compton shift

Question 12

When the angle of scattering is 90o, the Compton shift is found to be

Answer 12

0.0243 A

Question 12

What is the Physical significance of Compton Effect

Answer 12

*The phenomena of Compton effect is explained by Compton on the basis of
Quantum theory of radiation, in which it is assumed that radiation is composed
of small packets of energy called Quanta
*The Compton Effect is an elastic
collision between two particles namely photon and electron in which exchange
of energy takes place as if it is a particle–particle collision
* it is assumed that photon and electron obey laws of conservation of energy and momentum.
Hence Compton Effect signifies particle nature of radiation.

Question 12

what is the diff between a particle and a wave

Answer 12

*The concept of particle is easy to understand, because it has mass and occupies certain fixed position in space and particle in motion has definite momentum; when slowed down, it gives out energy. Therefore particle is specified by its mass, momentum, energy and position
*The concept of wave is bit difficult to understand, because a wave is a
disturbance spread over a large area. We cannot say wave is coming from here
or going there. No mass is associated with wave and the wave is characterized
by its wavelength, frequency, amplitude and phase.

Question 13

why is dual nature of both wave and particle accpeted

Answer 13

the phenomenon like interference and diffraction has shown beyond doubt the wave nature of light radiation
Huygens wave theory of light, however, experimental phenomenon like Photo electric effect, Compton Effect

Question 13

Explain De-Broglie concept of matter waves

Answer 13

According to this concept the dual characteristics of radiation is not confined
only to electromagnetic waves, but also holds good for all material particles in
motion i.e. all the particles like electrons, protons, neutrons, molecules, atoms
etc. exhibit dual characteristics
According to de-Broglie the particle in motion is associated with a group of
waves and controlled by the wave. This wave is known as matter wave or de
Broglie wave and wavelength associated with it is called de Broglie wavelength.

Question 14

Characteristics of Matter Waves

Answer 14

• Matter waves are the waves associated with a moving particle.
• The lighter the particle larger the wavelength.
• Smaller the velocity of particle larger the wavelength.
• The amplitude of the matter wave at a given point determines the
  probability of finding the particle at that point at a given instant of time.
• The wavelength of a particle is given by, λ= h/p = h/mv

Question 14

what is Phase velocity or wave velocity

Answer 14

If a point is imagined to be marked on a travelling wave, then it becomes a representative point for a particular phase of the wave and the velocity with which this point is transported owing to the motion of the wave is called phase velocity. The phase velocity is given in terms of the wave’s angular frequency ω and wave vector k by,
vp = ω/k

Question 15

derivation of phase velocity

Answer 15

y = asin(ωt-kx)
k=2pi/lamda
When phase is constant, (wt – kx) = constant.
Differentiating, w - k d x /dt = 0
dx/dt = ω/k dx/dt = phase velocity, vphase = ω/k

Question 16

what is group waves

Answer 16

The group velocity of a wave is the velocity with which the variations in the shape of the
wave’s amplitude (known as the modulation or envelope of the wave) propagate through
space. The group velocity is defined by the equation, vg = dow/dok

Question 17

derivation of group waves

Answer 17

y1 = asin(wt+kx)
y2=asint[(w + deltaw)t- (k+deltak)x]
y= y1+y2
after manipulation
y = 2A cos {(Δω/2)t – (Δk/2) x} sin (ωt – kx)
Comparing equation 1 and 3, the amplitude is cosine term (2A cos {(Δω/2)t – (Δk/2) x} ),
which is not a constant but varies as a wave. The velocity with it is transmitted is group
velocity given by, vgr = dω/dk.

Question 18

what is HEISENBERG’S UNCERTAINITY PRINCIPLE

Answer 18

in Quantum Mechanics the moving particle is described by a wave packet. The particles should be inside wave packet, hence when wave packet is small; position of the particle may be fixed, but particle flies off rapidly
due to very high velocity; hence, its momentum cannot be determined
accurately. When the wave packet is large, velocity or momentum may be
determined but position of particle becomes uncertain.
According to uncertainty principle it is impossible to determine precisely and
simultaneously, the exact values of both members of particular pair of physical
variables which describes atomic system.
In any simultaneous determination of position and momentum of a particle, the
product of corresponding uncertainties inherently present in the measurements
is equal to or greater than h/4π.
Δp.Δx ≥h/4π
ΔE.Δt ≥ h/4π
ΔL.Δθ≥ h/4π

Question 18

what is Normalized functions

Answer 18

The value of ׀ψ׀2 evaluated at point gives the probability of finding a particle at that point, hence the probability of finding the particle inan element of volume δv is given by ψδv
Since the particle must be somewhere in space, the total probability of finding the particle should be equal to 1 i.e Any function which obeys this condition is said to be normalized Wave function

Question 18

The deBroglie waves are pilot waves and are not electro-magnetic waves.

Answer 18

bbsbsnsns

Question 18

Applications of Heisenberg’s Uncertainty Principle

Answer 18

 Non-existence of electrons in nucleus of atoms
 Calculation of frequency of radiation emitted by atom
 Calculation of binding energy of an electron in an atom
 Determination of radius of Bohr electronic orbit

Question 19

Physical significance of Heisenberg’s uncertainty principle

Answer 19

Non-existence of electrons inside the nucleus of atoms.
 Calculation of frequency of radiation emitted by an atom.
 Calculation of binding energy of an electron in an atom.
 Determination of radius of Bohr electronic orbit.
 The wave and particle properties are complimentary to one another.
 It is impossible to determine precisely and simultaneously values of
physical variables which describes the atomic system.
The negatively charged particle electron cannot exist inside the nucleus. The
wave and particle properties are complimentary to one another rather than
contradictory.

Question 19

what is a Wave Function

Answer 19

The concept of wave function was introduced by Schrödinger in the matter wave equation. It is denoted by Ψ, it is a variable whose variations constitutes matter wave. Wave Function is related to position of particle

Question 19

characteristics of wave function

Answer 19

1) The wave function by itself has no direct physical significance.
2) The wave function cannot be interpreted by an experiment.
3) The wave function is complex quantity consisting of both real and
imaginary parts.
4) With the knowledge of the wave function we can establish angular
momentum, energy and position of particle.
5) The value of │Ψ I^2evaluated at point gives the probability of finding particle at that point

Question 19

what is Probability Density?

Answer 19

The product of ψ and ψ* is ψψ* = a 2 + b2, which is called Probability density denoted by P = ׀ψ׀2

Question 19

properties of a wave function

Answer 19

Property 1: Ψ is single valued everywhere
Property 2:Ψ is finite everywhere
Property 3:Ψ and its first derivatives with respect to its variable are continuous everywhere.
Property 4: For bound states, Ψ must vanish at infinity. If Ψ is a complex function, then
ΨΨ* must vanish at infinity

Question 19

conditions of normalized waves functions

Answer 19

Normalized wave functions should satisfy following conditions:
1. It should be single valued function.
2. It should be finite everywhere.
3. It should be continuous and it should have continuous first derivative
ψ tends to zero when x, y, z tends to 0.

Question 20

what are Eigen’s values

Answer 20

Eigen functions are used in Schrödinger equation to solve for energy of a
system, since there can only be certain restricted Eigen functions and hence
only few restricted values of energy, these values of energy is called Eigen
values of energy.

Question 21

derivation of Schrödinger Time Independent Wave Equation

Answer 21

do doo nigha page 21