1) The document discusses several topics in quantum mechanics including Planck's law, Wien's law, Rayleigh-Jeans law, Compton scattering, the Compton effect, de Broglie's hypothesis of matter waves, and the Davisson-Germer experiment. 2) It explains that Compton scattering results in a shift in wavelength when X-rays interact with electrons. Compton treated this as particle collision between photons and electrons. 3) The Davisson-Germer experiment in 1927 provided the first evidence of matter waves by observing interference patterns when electrons were diffracted by a nickel crystal, supporting de Broglie's hypothesis that particles can behave as waves.

1. Quantum Mechanics

7. Deduction of Radiation laws From Planck’s Law
I. Wien’s Law:
II. Rayliegh Jean’s Law
1) Rayleigh- jean’s law holds good when wavelength λ is large. (ν is small).
Thus Planck’s Law Reduces to Rayleigh- jean’s law

8. Compton scattering:
When a beam of high frequency radiation is scattered by a substance of low
atomic number the scattered radiations consists of two lines. One is having the
same wavelength λ as the incident beam. The other is having slightly longer
wavelength. This change in wavelength of the scattered X rays is known as the
Compton shift. This effect is called Compton Effect.
Theory of Compton Effect:
1. Compton treated this scattering as the interaction between X ray and the
matter as a particle collision between X ray photon and loosely bound
electron in the matter.
2. Consider an X ray photon of frequency ν striking an electron at rest.
3. This Photon is scattered through an angle ϴ to x-axis.
4. Let the frequency of the scattered photon be ν’
5. During collision the photon gives energy to the electron.
6. This electron moves with a velocity V at an angle φ to x axis.

13. Experimental verification of Compton Effect.
1. The experimental set up is as shown in the fig.
2. A beam of mono chromatic X ray beam is allowed to fall on the scattering material.
3. The scattered beam is received by a Bragg spectrometer.
4. The intensity of the scattered beam is measured for various angles of scattering.
5. A graph is plotted between the intensity and the wavelength.
6. Two peaks were found.
7. One belongs to unmodified and the other belongs to the modified beam.
8. The difference between the two peaks gives the shift in wavelength.
Experimental verification of Compton Effect

14. A Graph between wavelength and intensity of scattered x – rays

15. MATTER WAVES:
De Broglie’s Hypothesis:
1. Waves and particles are the modes of energy propagation.
2. Universe of composed of matter and radiations.
3. Since matter loves symmetry matter and waves must be symmetric.
4. If radiation like light which is a wave can act like particle some time, then materials like
particles can also act like wave some time.
Expression for de- Broglie Wavelength

16. Properties of Matter Waves
Davisson and Germer experiment
The first experimental evidence of matter waves was given by two American physicists,
Davisson and Germer in 1927. The experimental arrangement is shown in figure 1
The apparatus consists of an electron gun G where the electrons are produced. When the filament
of electron gun is heated to dull red electrons are emitted due to thermionic emissions. Now, the
electrons are accelerated in the electric field of known potential difference. These electrons are
collimated by suitable slits to obtain a fine beam which is then directed to fall on a large single
crystal of nickel, known as target T which is rotated about an angle along the direction of the
beam is detected by an electron detector (Faraday cylinder) which is connected to a
galvanometer. The Faraday cylinder ‘c’ can move on a circular graduated scale s between 29 °C
to 90 °C receive the scattered electrons.

17. Fig 1. Davisson and Germer’s experimental arrangement for verification of matter waves
First of all, the accelerating potential V is given a low value and the crystal is set at any orbital
azimuth (θ). Now the Faraday cylinder is moved to various positions on the scale’s’ and
galvanometer current is measured for each position. A graph is plotted between galvanometer
current against angle θ between incident beam and beam entering the cylinder [Figure3.1(b)].
The observations are repeated for different acceleration potentials.
Fig. 2. Variation of Galvanometer current with variation of angle θ between incident beam and
beam entering the cylinder
It is observed that a ‘bump’ begins to appear in the curve for 44 volts.
Following points are observed.
(a) With increasing potential, the bump moves upwards.
(b) The bump becomes most prominent in the curve for 54 volts at θ = 50
(c) At higher potentials, the bumps gradually disappear.
The bump in its most prominent state verifies the existence of electron waves.
According to de- Broglie, the wavelength associated with electron accelerated through a

18. potential V is given by
Hence, the wavelength associated with an electron accelerated through 54 volts is
From X-ray analysis, it is known that a nickel crystal acts as a plane diffraction grating
with space d = 0.91Å [see Figure 3]. According to experiment, we have diffracted electron beam
at θ = 50°. The corresponding angle of incidence relative to the family of Bragg plane.
As the two values are in good agreement, hence, confirms the de-Broglie concept of matter
waves.