B1. The electromagnetic spectrum

Light (the visible spectrum) is only a small part of the electromagnetic spectrum. Electromagnetic radiation travels as electromagnetic waves that differ in wavelength (λ) and frequency (ν). All of them travel at the same speed in vacuum, c = 3 × 10⁸ m/s, so:

c = λ ν

The spectrum, from longest to shortest wavelength: radio waves → microwaves → infrared → visible light → ultraviolet → X-rays → gamma rays. As the wavelength becomes shorter the frequency and the energy of each photon become greater (E = hν).

Visible light

• is made of the spectrum colours, in order: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV).
• Red has the longest wavelength (about 700 nm) and violet the shortest (about 400 nm).

Problem. Calculate the frequency of red light (λ = 700 nm) and blue light (λ = 450 nm), and the energy of one photon of blue light (h = 6.63 × 10⁻³⁴ J·s).

Solution. ν = c/λ. Red: 3 × 10⁸ ÷ 700 × 10⁻⁹ = 4.29 × 10¹⁴ Hz. Blue: 3 × 10⁸ ÷ 450 × 10⁻⁹ = 6.67 × 10¹⁴ Hz. E = hν = 6.63 × 10⁻³⁴ × 6.67 × 10¹⁴ = 4.42 × 10⁻¹⁹ J. Blue photons have about 1.56 times the energy of red photons (700/450).