understand that electromagnetic radiation has a particulate nature

Energy and Momentum of a Photon

Light isn’t just a wave – it’s also made of tiny packets called photons. Think of a photon like a tiny, invisible ball of energy that can bounce off objects, just like a ball can bounce off a wall. This dual nature (wave & particle) is a key idea in modern physics.

What is a Photon?

A photon is the smallest possible unit (quantum) of electromagnetic radiation. It behaves like a particle when it interacts with matter (e.g., knocks an electron out of an atom) but also shows wave-like properties (interference, diffraction).

Energy of a Photon

The energy carried by a photon depends on its frequency:

\$E = h\nu\$

  • \$h\$ = Planck’s constant ≈ \$6.626\times10^{-34}\,\text{J·s}\$

  • \$\nu\$ = frequency of the light (Hz)

  • Higher frequency → more energy (e.g., X‑rays > visible light)

Example: A green photon (\$\lambda\approx520\,\text{nm}\$) has a frequency \$\nu=c/\lambda\approx5.8\times10^{14}\,\text{Hz}\$, giving \$E\approx3.8\times10^{-19}\,\text{J}\$.

Momentum of a Photon

Even though photons have no rest mass, they carry momentum:

\$p = \frac{h}{\lambda}\$

  • \$\lambda\$ = wavelength of the photon

  • Shorter wavelength → larger momentum (e.g., gamma rays push harder than radio waves)

This momentum explains phenomena like Compton scattering, where photons bounce off electrons and change direction.

Why Photons are Particles

Key experiments that show the particle nature:

  1. Photoelectric effect – Light ejects electrons from a metal only if its frequency is high enough, regardless of intensity.

  2. Compton scattering – Photons collide with electrons, transferring energy and momentum.

  3. Black‑body radiation – Planck’s model uses quantised energy packets to explain the spectrum.

These experiments confirm that light behaves as discrete particles, not just waves.

Summary Table

PropertyFormulaUnits
Energy\$E = h\nu\$Joules (J)
Momentum\$p = \dfrac{h}{\lambda}\$kg·m/s
Frequency–Wavelength Relation\$\nu = \dfrac{c}{\lambda}\$Hz

Exam Tips 📚

  • Remember the key formulas: \$E = h\nu\$ and \$p = h/\lambda\$.

  • Use the relation \$\nu = c/\lambda\$ to switch between frequency and wavelength.

  • When given energy, find frequency: \$\nu = E/h\$.

  • For momentum problems, always check units – momentum is in kg·m/s.

  • Practice converting between J, eV, and Hz (1 eV ≈ 1.602×10⁻¹⁹ J).

  • Use the photoelectric effect diagram to explain why intensity doesn’t affect threshold frequency.