Unit 1: Elements of Modern Physics

Table of Contents

1. Failure of Classical Physics & Planck's Hypothesis

By the late 19th century, classical physics could not explain the Blackbody Radiation spectrum (leading to the "Ultraviolet Catastrophe").

In 1900, Max Planck proposed that energy is not continuous but exchanged in discrete packets called Quanta.

E = h ν

Where h is Planck's constant (6.626 × 10-34 J·s) and ν is the frequency.

2. Photoelectric Effect

The Photoelectric Effect is the emission of electrons from a metal surface when light of a sufficient frequency shines on it. Classical theory failed because it predicted that emission should depend on intensity, not frequency.

Einstein’s Photoelectric Equation:

Einstein applied Planck's idea, suggesting light itself consists of particles called Photons.

h ν = Φ + Kmax

Where Φ (Work Function) is the minimum energy required to liberate an electron, and Kmax is the maximum kinetic energy of the emitted electron.

3. Compton Effect

Arthur Compton observed that when X-rays are scattered by a material (like graphite), the scattered radiation has a longer wavelength than the incident radiation. This shift depends on the scattering angle.

Compton Shift Formula:

Δ λ = λ' - λ = (h) / (m0 c) (1 - cos θ)

This experiment proved that photons carry linear momentum and behave like particles during collisions.

4. Wave-Particle Duality & de Broglie Waves

In 1924, Louis de Broglie hypothesized that if light (a wave) can behave like a particle, then matter (particles) should also behave like waves.

λ = (h) / (p) = (h) / (mv)

This is known as the de Broglie wavelength. It suggests that every moving object has an associated "matter wave."

5. Davisson-Germer Experiment

This experiment provided the first direct evidence for the wave nature of electrons. By scattering an electron beam off a Nickel crystal, they observed diffraction patterns similar to X-rays.

Key Result: The measured wavelength of the diffracted electrons perfectly matched the value predicted by de Broglie's formula.

6. Phase Velocity and Group Velocity

A matter wave is represented by a Wave Packet (a superposition of many waves with slightly different frequencies).

vg = (dω) / (dk)

In quantum mechanics, the group velocity of a particle's wave packet is equal to the classical velocity of the particle.

Exam Focus Corner

Frequently Asked Questions

Common Mistakes

Exam Tips

Tip: If asked to differentiate between Photoelectric and Compton effects, remember: Photoelectric involves complete absorption of the photon, while Compton involves scattering with energy transfer.