recall and use E = hf

Energy and Momentum of a Photon 📚

What is a Photon?

A photon is a tiny packet of light energy that travels at the speed of light, c = 3.00 × 10⁸ m/s. Think of it as a “light bullet” that carries energy and momentum but has no mass.

Key Formula: Energy of a Photon

The energy of a photon is directly proportional to its frequency:



\$E = hf\$



where \$h = 6.626 \times 10^{-34}\,\text{J·s}\$ is Planck’s constant and \$f\$ is the frequency in hertz (Hz).



Analogy: Imagine a musical note. The higher the note (frequency), the louder it sounds (energy). A photon’s “loudness” is its energy.

Momentum of a Photon

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



\$p = \dfrac{E}{c} = \dfrac{hf}{c}\$



Example: A photon with energy 3.3 × 10⁻¹⁹ J has a momentum of about 1.1 × 10⁻²⁷ kg·m/s.

Quick Reference Table

Frequency (Hz)Energy (J)
5 × 10¹⁴ Hz (visible light)≈ 3.3 × 10⁻¹⁹ J
1 × 10¹⁴ Hz (infrared)≈ 6.6 × 10⁻²⁰ J
1 × 10¹⁵ Hz (ultraviolet)≈ 6.6 × 10⁻¹⁹ J

Exam Tips for A-Level Physics 9702 🎓

  1. Always write down the value of Planck’s constant: \$h = 6.626 \times 10^{-34}\,\text{J·s}\$.
  2. Check units: frequency is in Hz (s⁻¹), energy in J (kg·m²/s²).
  3. When converting between energy and momentum, use \$p = E/c\$ and remember that c = 3.00 × 10⁸ m/s.
  4. Use the analogy of a “light bullet” to explain why photons have momentum even though they have no mass.
  5. For numerical problems, round your answer to the correct number of significant figures.