Electromagnetic spectrum

AS Level Physics · Waves. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

All electromagnetic waves are transverse waves. In free space (a vacuum) they all travel at the same speed, c = 3.00 × 108 m s−1. They do not need a medium.

The regions of the spectrum differ only in wavelength and frequency. In order of decreasing wavelength they are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and γ-rays. Because c is fixed, a shorter wavelength always means a higher frequency.

You must know the rough wavelength range of each region, and that the eye sees only wavelengths from about 400 nm (violet) to 700 nm (red). The ranges of X-rays and γ-rays overlap.

Rules to remember

Common mistake

Students mix up the two ends of the spectrum. Radio waves have the longest wavelength and lowest frequency; γ-rays have the shortest wavelength and highest frequency.

Worked example

An electromagnetic wave has a frequency of 6.0 × 1013 Hz in free space. In which region of the spectrum is it? (c = 3.00 × 108 m s−1)

  1. Wavelength λ = c ÷ f = (3.00 × 108) ÷ (6.0 × 1013) = 5.0 × 10−6 m
  2. This is longer than red light (7 × 10−7 m) and shorter than 10−3 m
  3. That range is infrared

Answer: Infrared (wavelength 5.0 × 10−6 m)

Practice questions

Try each one, then open the answer.

1. A radio wave has a wavelength of 3.0 m. What is its frequency in a vacuum? (c = 3.0 × 108 m/s)

  1. A
    1.0 × 106 Hz
  2. B
    1.0 × 107 Hz
  3. C
    1.0 × 108 Hz
  4. D
    9.0 × 108 Hz
Show answer

Answer: C. f = c/λ = 3.0 × 108 ÷ 3.0 = 1.0 × 108 Hz (100 MHz, FM radio).

2. Which list gives regions of the electromagnetic spectrum in order of increasing wavelength?

  1. A
    radio waves, infrared, ultraviolet, γ-rays
  2. B
    ultraviolet, γ-rays, infrared, microwaves
  3. C
    γ-rays, ultraviolet, infrared, radio waves
  4. D
    X-rays, visible light, ultraviolet, radio waves
Show answer

Answer: C. From shortest to longest: γ-rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves.

3. An electromagnetic wave has a frequency of 1.0 × 1015 Hz in free space. In which region of the spectrum is it? (c = 3.00 × 108 m s−1)

  1. A
    microwaves
  2. B
    infrared
  3. C
    visible light
  4. D
    ultraviolet
Show answer

Answer: D. λ = c/f = 3.00 × 108 ÷ 1.0 × 1015 = 3.0 × 10−7 m = 300 nm. This is shorter than 400 nm, the violet end of the visible range, so it is ultraviolet.

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