The Electromagnetic Spectrum: Quick Revision

A brief note on The Electromagnetic Spectrum. Read it before a test. Try each question at the end before you open its answer.

The bands

• Order of rising frequency: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
• Same speed: all travel at $c = 3.00 \times 10^{8}$ m/s in vacuum, with $c = f\lambda$.
• Photon energy: $E = hf = 1240/\lambda$ eV for $\lambda$ in nm. It rises with the frequency.
• Ranges used here: radio above $0.1$ m; microwave $1$ mm to $0.1$ m; infrared $700$ nm to $1$ mm; visible $400$ nm to $700$ nm; ultraviolet $1$ nm to $400$ nm; X-ray $10^{-3}$ nm to $1$ nm; gamma below $10^{-3}$ nm.

Sources, detectors and uses

• Radio: accelerated charges in an antenna. Broadcasting and mobile phones.
• Microwave: magnetron and klystron tubes. Radar, satellites and ovens. Radar: $d = ct/2$.
• Infrared: hot bodies. Thermal cameras and remote controls.
• Visible and ultraviolet: electrons in atoms. UV sterilises and can harm cells.
• X-rays: fast electrons stopped in metal. $\lambda_{\min} = hc/eV$.
• Gamma: nuclei. Treating cancer and sterilising.
• Wien's law: $\lambda_{peak}T = 2.898 \times 10^{-3}$ m K.

The atmosphere

• Ozone takes in UV-B and UV-C. UV photons can break chemical bonds.
• Greenhouse gases take in the infrared of the ground. They warm the Earth from about $255$ K to $288$ K.
• Ionosphere: returns waves below $f_c = 9\sqrt{N}$ (Hz, $N$ in m⁻³), and below $f_c/\cos i$ at an angle $i$.
• Waves: ground (low frequency), sky (short wave, by the ionosphere), space (straight line, $d = \sqrt{2Rh}$).

A worked example

A star has a surface temperature of $4500$ K. A radio link uses a wave of wavelength $0.45$ m. Find the peak wavelength of the star and the frequency of the link.

1. The star. $\lambda_{peak} = \dfrac{2.898 \times 10^{-3}\ \text{m K}}{4500\ \text{K}} = 644$ nm, which is in the visible band (green to yellow).
2. The link. $f = \dfrac{3.00 \times 10^{8}\ \text{m/s}}{0.45\ \text{m}} = 667$ MHz.

Practise with new numbers

Check yourself

1. Which band is sent out by a warm body and takes in water, and which band has the highest photon energy?

2. Why does the ionosphere not return FM radio and television waves?

3. What does the ozone layer do for life on Earth?

Sources

• OpenStax, University Physics Volume 2, Chapter 16 (Electromagnetic Waves).
• NCERT Physics Class 12, Chapter 8 (Electromagnetic Waves).