Advanced · 14 min
Photons and light energy
Connect light frequency, wavelength, and the energy of a single photon.
Light transfers energy in packets
A photon is a quantum of electromagnetic radiation. Its energy is E = h × f, where f is frequency and h is Planck's constant, approximately 6.6 × 10⁻³⁴ J·s for these calculations. Higher frequency means more energy per photon. Light can show wave behaviour, such as interference, while its energy is exchanged in discrete amounts. More intense light at a fixed frequency can contain more photons without changing each photon's energy.
Worked example
For f = 4 × 10¹⁴ Hz: E = 6.6 × 10⁻³⁴ × 4 × 10¹⁴ = 2.64 × 10⁻¹⁹ J
Wavelength connects to frequency
In vacuum, c = f × λ, so photon energy can also be written E = h × c ÷ λ. A shorter vacuum wavelength means a higher frequency and more energy per photon. Convert nanometres before using metres per second: 1 nm = 10⁻⁹ m. Scientific notation separates a coefficient from a power of ten. These questions state when to enter only that coefficient, so you do not need to type powers into the answer box.
Worked example
For vacuum wavelength 750 nm and c = 3 × 10⁸ m/s: f = (3 × 10⁸) ÷ (750 × 10⁻⁹) = 4 × 10¹⁴ Hz
Compare two colours mathematically
- Using c = 3 × 10⁸ m/s, compare the frequencies for vacuum wavelengths of 400 nm and 800 nm.
- Use E = h × f to find the ratio of their photon energies. Explain why the shorter wavelength has more energy per photon.