Comprehensive notes for Chapter 19 Dawn of Modern Physics. Covers Special Theory of Relativity, Black Body Radiation, Photoelectric Effect, Compton Effect, Pair Production, De Broglie Wavelength, and Heisenberg Uncertainty Principle.
Postulates: 1. Laws of physics are same in all inertial frames. 2. Speed of light (c) is constant.
Results:
Stefan-Boltzmann Law: Total energy radiated $$ E = \sigma T^4 $$.
Wien's Displacement Law: $$ \lambda_{max} \times T = \text{Constant} (2.9 \times 10^{-3} mK) $$.
Planck's Assumption: Energy is quantized. $$ E = hf $$, where h is Planck's constant ($$ 6.63 \times 10^{-34} Js $$).
Emission of electrons from metal surface when light shines on it. Proves particle nature of light.
Einstein's Equation: $$ hf = \phi + K.E_{max} $$ where $$ \phi $$ is Work Function.
Threshold Frequency ($$ f_0 $$): Minimum frequency required for emission.
Increase in wavelength of X-rays when scattered by loosely bound electrons. Proves particle nature of radiation.
Compton Shift ($$ \Delta \lambda $$): $$ \Delta \lambda = \frac{h}{m_0 c} (1 - \cos \theta) $$.
Where $$ \frac{h}{m_0 c} $$ is Compton Wavelength ($$ 2.43 \times 10^{-12} m $$).
Pair Production: High energy photon ($$ > 1.02 MeV $$) converts into electron-positron pair near heavy nucleus. $$ hf = 2m_0 c^2 + K.E $$.
Annihilation: Electron and positron combine to produce two gamma ray photons moving in opposite directions. $$ e^- + e^+ \rightarrow \gamma + \gamma $$.
De Broglie Wavelength ($$ \lambda $$): Particles have wave-like properties. $$ \lambda = \frac{h}{p} = \frac{h}{mv} $$. Confirmed by Davisson and Germer Experiment (Electron Diffraction).
It is impossible to measure position and momentum simultaneously with perfect accuracy.
Position-Momentum: $$ \Delta x \cdot \Delta p \approx h $$
Energy-Time: $$ \Delta E \cdot \Delta t \approx h $$