Electromagnetic Spectrum Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Electromagnetic Spectrum.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The complete continuum of all electromagnetic waves, organized in order of increasing frequency (or decreasing wavelength).

A 'rainbow' that extends far beyond visible light in both directions.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Electromagnetic Spectrum asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to electromagnetic spectrum but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?

Worked Examples

Example 1

easy
Arrange the following EM waves from lowest to highest frequency: visible light, X-rays, radio waves, ultraviolet, infrared, gamma rays, microwaves.

Answer

Radio<Microwave<IR<Visible<UV<X-ray<Gamma\text{Radio} < \text{Microwave} < \text{IR} < \text{Visible} < \text{UV} < \text{X-ray} < \text{Gamma}

First step

1
The electromagnetic spectrum from lowest to highest frequency: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.

Full solution

  1. 2
    This is also the order from longest to shortest wavelength.
  2. 3
    All travel at the same speed (c=3×108 m/sc = 3 \times 10^8 \text{ m/s}) in a vacuum.
The electromagnetic spectrum encompasses all EM waves ordered by frequency (or wavelength). Higher frequency means shorter wavelength and more energy per photon. All EM waves travel at the speed of light.

Example 2

medium
A photon of ultraviolet light has a wavelength of 200 nm200 \text{ nm}. What is its energy? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s} and h=6.626×10−34 J sh = 6.626 \times 10^{-34} \text{ J s}.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A cell phone operates at 800 MHz800 \text{ MHz} and an X-ray machine at 3×1018 Hz3 \times 10^{18} \text{ Hz}. By what factor is the X-ray frequency greater than the cell phone frequency?

Example 2

hard
The human eye detects light from 380 nm380 \text{ nm} (violet) to 700 nm700 \text{ nm} (red). What is the range of frequencies for visible light? What fraction of the full EM spectrum (from 3 Hz3 \text{ Hz} radio to 3×1020 Hz3 \times 10^{20} \text{ Hz} gamma) does visible light occupy? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s}.

Example 3

easy
List the main regions of the EM spectrum in order of increasing frequency.

Example 4

easy
Which has a longer wavelength: radio waves or X-rays?

Example 5

easy
As frequency increases across the EM spectrum, what happens to wavelength?

Example 6

easy
Which region of the EM spectrum can the human eye detect?

Example 7

easy
Within visible light, which color has the highest frequency: red or violet?

Example 8

easy
Which EM region lies just beyond the red end of visible light, at lower frequency?

Example 9

easy
Which EM region lies just beyond the violet end of visible light, at higher frequency?

Example 10

easy
Do all regions of the EM spectrum travel at the same speed in vacuum?

Example 11

medium
An EM wave has frequency 5×10165\times10^{16} Hz. Which spectral region is it (UV: ~101510^{15}-101710^{17} Hz)?

Example 12

medium
A gamma ray has wavelength 3×10−123\times10^{-12} m. Find its frequency in vacuum.

Example 13

medium
Order these by increasing wavelength: X-ray, microwave, visible light.

Example 14

medium
Red light is about 700700 nm, blue about 450450 nm. Which has higher frequency?

Example 15

medium
An FM radio wave at 100100 MHz: find its wavelength in vacuum.

Example 16

medium
Microwaves and visible light: which has the higher photon-relevant frequency, and is it higher or lower energy region?

Example 17

medium
A wave region spans wavelengths 11 mm to 11 m. Compute the frequency at the 11 mm end.

Example 18

medium
Which carries more energy per photon: an infrared wave or an X-ray?

Example 19

medium
Infrared and radio waves: which has the shorter wavelength?

Example 20

challenge
A telescope detects a 2121 cm radio line from hydrogen. Find its frequency in MHz.

Example 21

challenge
Two EM waves differ in frequency by a factor of 1000. By what factor do their wavelengths differ?

Example 22

challenge
Sunlight peaks near 500500 nm (visible). A star peaks at 100100 nm. Which region is the star's peak, and is the star hotter or cooler than the Sun (peak wavelength shorter for hotter)?

Example 23

easy
Which has higher frequency: infrared or ultraviolet?

Example 24

easy
A radio wave has frequency 98 MHz98\,\text{MHz}. Find its wavelength in vacuum.

Example 25

easy
Sort by increasing wavelength: gamma, visible light, microwave.

Example 26

easy
A microwave has wavelength 12 cm12\,\text{cm}. Find its frequency.

Example 27

medium
A radio wave has λ=1.5 m\lambda = 1.5\,\text{m}. Find its frequency in MHz.

Example 28

medium
An EM wave has wavelength 1 μm1\,\mu\text{m} (10−6 m10^{-6}\,\text{m}). Which spectral region is it in?

Example 29

medium
A photon has frequency f=5×1014 Hzf = 5\times10^{14}\,\text{Hz}. Find its wavelength and identify the region.

Example 30

medium
An ultraviolet wave has frequency 1×1016 Hz1\times10^{16}\,\text{Hz}. Find its wavelength in nm.

Example 31

medium
A cell phone tower transmits at 2.0 GHz2.0\,\text{GHz}. Find the wavelength.

Example 32

medium
An EM wave with λ=1 nm\lambda = 1\,\text{nm} — which region is it?

Example 33

medium
A wave at λ=50 cm\lambda = 50\,\text{cm} is most likely in which region?

Example 34

medium
What is the wavelength of a 2.4 GHz2.4\,\text{GHz} Wi-Fi signal?

Example 35

hard
The visible spectrum runs from about 400 nm to 700 nm. Find the corresponding frequency range.

Example 36

hard
A photon has energy 4×10−19 J4\times10^{-19}\,\text{J}. Use h=6.63×10−34 J\cdotpsh = 6.63\times10^{-34}\,\text{J·s} to find its frequency and region.

Example 37

hard
Two stars: star A peaks at λ=600 nm\lambda = 600\,\text{nm}, star B peaks at λ=300 nm\lambda = 300\,\text{nm}. Using Wien's displacement law (λmaxT=\lambda_{max}T = const), find the ratio of B's surface temperature to A's.

Example 38

hard
A satellite transmits at λ=5 cm\lambda = 5\,\text{cm}. Is this radio, microwave, or infrared?

Example 39

challenge
A medical X-ray has λ=0.05 nm\lambda = 0.05\,\text{nm}. Find its photon energy in electronvolts. (Use hc≈1240 eV\cdotpnmhc \approx 1240\,\text{eV·nm}.)
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Background Knowledge

These ideas may be useful before you work through the harder examples.

electromagnetic wavesfrequencywavelength