The electromagnetic spectrum

Visible light is part of the electromagnetic (EM) spectrum - which includes all possible EM frequencies from radio waves to gamma rays.

All electromagnetic radiation travels at the speed of light, c = 3 x 10^8^ m s^-1^.

The shorter the wavelength, the higher the frequency.

Shorter wavelength radiation carries more energy.

Electromagnetic radiation travels in discrete photons

Electromagnetic radiation propagates in discrete bundles called photons.

Each photon carries a quantum of EM energy related to the frequency by Planck's constant:

E = h f

Where:

E = photon energy in J

h = Planck's constant (6.63 x 10^-34 J s)

f = frequency (Hz)

We also know:

$ c = f \lambda $

Where:

c = speed of light (3 x 10⁸ m s^-1)

f = frequency (Hz)

λ = wavelength (m)

Combining these gives an equation for photon energy in terms of wavelength:

$ \text{E = }\frac{\text{h c}}{\lambda} $

Photons are discrete packets of EM radiation with energy proportional to their frequency or inversely proportional to their wavelength.

Worked Example 1 - Calculating photon energy

Calculate the energy of a photon with a frequency of 6 x 10¹⁴ Hz.

Step 1: Formula

$E = h f$

Step 2: Substitution and correct evaluation

E = 6.63 x 10^-34 x 6 x 10¹⁴ = 3.978 x 10^-19 J

Worked Example 2 - Calculating photon wavelength

Calculate the wavelength of a photon which has an energy of 1.02 x 10^-16 J.

Step 1: Formula

$\text{E = }\frac{\text{h c}}{\lambda}$

Step 2: Rearrangement

$\lambda = \frac{h c}{E}$

Step 3: Substitution and correct evaluation

$\lambda = \frac{6.63 \times 10^{-34}\times 3 \times 10^8}{1.02 \times 10^{-16}}= 1.95 \times10^{-9}\text{ m}$