3.2.1.3

A photon is a quantum of electromagnetic energy

Particles, Antiparticles & Photons — AQA A-Level Physics

Key Definition
Photon — A massless discrete packet (quantum) of electromagnetic energy.
$$\begin{aligned} E &= hf \\ &= \frac{hc}{\lambda} \end{aligned}$$
$$E = hf$$
  • $E$: energy of the photonA quantum (discrete packet) of electromagnetic radiation. Its energy is proportional to its frequency. (J)
  • $h$: Planck's constant (6.63 × 10⁻³⁴ J s)
  • $f$: frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). (Hz)
$$E = \frac{hc}{\lambda}$$
  • $E$: energy of the photon (J)
  • $h$: Planck's constant (J s)
  • $c$: speed of light (3.00 × 10⁸ m s⁻¹)
  • $λ$: wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). (m)
Worked Example
Light of wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). 490 nm and powerThe rate of energy transfer. Measured in watts (W). 3.6 mW is incident on a surface and completely absorbed. Calculate the number of photons hitting the surface in 2.0 s.
Show Solution
1
List known values
  • $\lambda = 490 \times 10^{-9}$ m
  • $P = 3.6 \times 10^{-3}$ W
  • $t = 2.0$ s
2
Calculate the energy of one photon

$$E = \frac{hc}{\lambda} = \frac{(6.63 \times 10^{-34}) \times (3.0 \times 10^{8})}{490 \times 10^{-9}} = 4.06 \times 10^{-19} \text{ J}$$

3
Find photons per second

$$\frac{P}{E} = \frac{3.6 \times 10^{-3}}{4.06 \times 10^{-19}} = 8.9 \times 10^{15} \text{ s}^{-1}$$

4
Multiply by time

$$N = 8.9 \times 10^{15} \times 2.0 = 1.8 \times 10^{16}$$

Answer
$N = 1.8 \times 10^{16}$ photons
Examiner Tips and Tricks
  • Learn the definition: 'a discrete quantity/packet/quantum of electromagnetic energy'.
  • Planck's constant and the speed of light are on the data sheet, but memorising them speeds up calculation questions.
Particles, Antiparticles & Photons Overview