Unit - I Modern Physics

1. Unit - IModern Physics Dr. Ravindra & Dr. P.S. Aithal

2. Objectives • The failures of classical mechanics and origin of Quantum mechanical theory • The application of quantum idea to explain black body radiation spectrum, photoelectric effect and Compton effect • The de-Broglie hypothesis (matter waves) and experimental evidence given by Davison and Germer • The relation between the group velocity, phase velocity, particle velocity and velocity of light • Characteristics of matter waves

3. Introduction to Modern Physics • All theories developed before the arrival of relativity and quantum mechanics and any work derived from them are called Classical physics. • All theories derived from the basic principles of relativity and quantum mechanics are called Modern physics.

4. Blackbody Radiation • Black body - An object that absorbs all the frequencies of electromagnetic radiation falling on it

5. Energy Distribution in Blackbody Radiation Spectrum Characteristics of Blackbody radiation spectrum • The energy is not uniformly distributed with frequency. • At a given temperature, the energy density initially increases with increase in frequency reaches a maximum value and then decreases with further increase in frequency. • The frequency corresponding to the maximum energy density (peak of the curve) shifts towards higher frequency side with increase in temperature.

6. Laws of Blackbody Radiation • Stefan law • Wein’s Distribution Law • Wein’s Exponential Law where A and β are Wien’s constants

7. Limitations of Wein’s Law

8. Rayleigh –Jeans Law • According to Lord Rayleighand James Jeans, the spectral energy density at frequency range f and f+df is simply the density of modes multiplied by kBT, where kB is Boltzmann’s constant = 1.380 x10-23 J/K. • Limitations of Rayleigh –Jeans Law : The Ultraviolet Catastrophe

9. Planck’s Radiation Law • Deduction of Weins law from Planck’s radiation law Weins law valid only in the higher frequency region i.e For high frequency region is very large

10. Deduction of Rayleigh-Jeans law from Planck’s radiation law R-J law valid only in the lower frequency region i.e • f is small implies is very small and expand as power series

11. Photo-electric Effect • emission of electrons from a metal surface when illuminated by light of suitable frequency • Discovered by H. Hertz in 1887.

12. Einstein’s Photoelectric Equation hf =  + ½ mv2max

13. Compton Effect • When X-rays of sharply defined frequency are incident on a material of low atomic number like carbon, they suffer a change of frequency on scattering. The scattered beam contains two wavelengths. In addition to the expected incident wavelength, there exists a component of longer wavelength. This phenomenon is called Compton effect. • The change in wavelength (∆λ) from incident wavelength (λ) to longer wavelength (λ’) is called Compton shift.

15. de-Broglie Hypothesis • λ = h/mv

16. Davison and Germer Experiment

17. Phase velocity, group velocity and Particle velocity • Phase velocity : The velocity with which the phase of the vibrating particle propagates as the wave progresses is called phase velocity • Group velocity: The velocity with which the wave packet, formed due to the superposition of two or more travelling waves of slightly different frequency, is transported is called group velocity.

18. Relation between phase velocity and group velocity

19. Relation between group velocity and particle velocity

20. Relation between velocity of light, group velocity and phase velocity

21. Expression for De-Broglie wavelength using group velocity

22. Characteristics of matter waves • The waves associated with moving particle are called matter waves • The amplitude of the matter waves at a particular region and time depends on the probability of finding the particle at the same region and time. • The group velocity is same as the particle velocity and the group velocity is always lesser than the velocity of light. Thus the phase velocity of the matter wave is always greater than the velocity of light. • The wave velocity of matter waves may differ depending on the mass and velocity of the particle. But the electromagnetic waves always travel with a constant velocity.