← Wave Systems
9 The electromagnetic spectrum
Visible light is one small band of a much wider family of waves, all of which are oscillating electric and magnetic fields that need no medium and travel at the same speed, c, in a vacuum.The spectrum, long wavelength to short
- radio → microwave → infra-red → visible (red → orange → yellow → green → blue → violet) → ultraviolet → X-ray → gamma.
- Wavelength DECREASES and frequency INCREASES left to right along that list — they are inversely related at fixed speed c = fλ.
- All of them travel at the same speed c in a vacuum; only λ and f differ from one part of the spectrum to another.
Photon energy
Wave speed (vacuum) c=f\lambda c = 3.00 × 10⁸ m s⁻¹. Photon energy E=hf h = Planck's constant, 6.63 × 10⁻³⁴ J s. Higher frequency (shorter λ) ⟹ higher-energy photons. Worked example Comparing photon energies A radio wave has wavelength 300 m and a gamma ray has wavelength 3.00 × 10⁻¹³ m. Find the ratio of the gamma ray's photon energy to the radio wave's. E = hf = hc/λ, so E is inversely proportional to λ at fixed c. Ratio of energies = ratio of wavelengths inverted: E_gamma / E_radio = λ_radio / λ_gamma. E_gamma / E_radio = 300 / (3.00×10⁻¹³) = 1.00 × 10¹⁵. ✓ The gamma-ray photon carries 10¹⁵ times more energy than the radio-wave photon, despite both travelling at the same speed c.Why this matters beyond the formula
- Higher-energy photons (UV, X-ray, gamma) can ionise atoms and damage tissue; lower-energy photons (radio, microwave, infra-red) generally cannot.
- This is the same E = hf relationship used for the photoelectric effect: a photon either has enough energy to eject an electron or it does not, regardless of how many low-energy photons arrive.