Electromagnetic Waves, Wavelength, and Frequency
Electromagnetic waves are oscillating electric and magnetic fields that travel through space at the speed of light, c = 3.00 × 108 m/s, and their wavelength (λ) and frequency (ν) are related by c = λν. In brief: green light of wavelength 520 nm has a frequency of 3.00 × 108 / 520 × 10−9 = 5.77 × 1014 Hz, and an FM radio station at 100 MHz broadcasts at a wavelength of 3.00 m.
The spectrum of electromagnetic radiation runs from radio waves to gamma rays, and what distinguishes them is only the wavelength (or frequency). Chemists use the interaction of radiation with atoms and molecules to find out their structure. This article defines the properties of a wave, shows the electromagnetic spectrum in a table, explains the relation between wavelength and frequency with worked examples and covers the history of the discovery.
What are the properties of a wave?
- Wavelength (λ): the distance between two successive crests. The SI unit is the meter, but nanometers (1 nm = 10−9 m), micrometers and angstroms (1 Å = 10−10 m) are often used.
- Frequency (ν): the number of complete waves that pass a point per second, in hertz (Hz = s−1).
- Amplitude: the height of the crest, related to the intensity (the energy carried per second per area is proportional to the square of the amplitude).
- Speed: in a vacuum, all electromagnetic waves travel at c = 2.998 × 108 m/s (often rounded to 3.00 × 108 m/s). In a medium, the speed is lower, by the factor n, the refractive index.
- Wavenumber (ṽ): 1/λ, usually in cm−1, used in infrared spectroscopy.
How are wavelength and frequency related?
Since the wave advances by one wavelength in the time of one cycle, the speed is the product of the wavelength and frequency:
c = λ × ν, so ν = c / λ and λ = c / ν
The longer the wavelength, the lower the frequency. In the formula, λ must be in meters to get ν in Hz. Light is a transverse wave in which the electric and magnetic fields oscillate at right angles to each other and to the direction of travel, and it needs no medium: it travels through a vacuum.
What is the electromagnetic spectrum?
| Region | Wavelength | Frequency (Hz) | Typical sources and uses |
|---|---|---|---|
| Radio | > 1 m | < 3 × 108 | Broadcasting, NMR |
| Microwave | 1 mm – 1 m | 3 × 108 – 3 × 1011 | Radar, microwave ovens, mobile phones |
| Infrared | 700 nm – 1 mm | 3 × 1011 – 4.3 × 1014 | Heat, molecular vibrations |
| Visible | 400 – 700 nm | 4.3 × 1014 – 7.5 × 1014 | Vision, photosynthesis |
| Ultraviolet | 10 – 400 nm | 7.5 × 1014 – 3 × 1016 | Sunburn, sterilization |
| X-rays | 0.01 – 10 nm | 3 × 1016 – 3 × 1019 | Medical imaging, crystallography |
| Gamma rays | < 0.01 nm | > 3 × 1019 | Radioactive decay, cancer therapy |
The boundaries are conventions and differ between sources; the regions merge into each other. The visible region, to which our eyes respond, is only a very narrow band of the spectrum.
What are the colors of visible light?
| Color | Wavelength (nm) | Frequency (1014 Hz) |
|---|---|---|
| Violet | 380–450 | 6.7–7.9 |
| Blue | 450–495 | 6.1–6.7 |
| Green | 495–570 | 5.3–6.1 |
| Yellow | 570–590 | 5.1–5.3 |
| Orange | 590–620 | 4.8–5.1 |
| Red | 620–750 | 4.0–4.8 |
Worked examples
Example 1: frequency of green light
ν = c / λ = 3.00 × 108 m/s / (520 × 10−9 m) = 5.77 × 1014 Hz.
Example 2: wavelength of a radio station
An FM station broadcasts at 100.0 MHz = 1.000 × 108 Hz. λ = 3.00 × 108 / 1.000 × 108 = 3.00 m.
Example 3: a microwave oven
Microwave ovens use a frequency of 2.45 GHz = 2.45 × 109 Hz, and the wavelength is λ = 3.00 × 108 / 2.45 × 109 = 0.122 m = 12.2 cm. This frequency is absorbed by water molecules, which rotate to follow the oscillating field, and the rotation heats the food.
Example 4: converting units
An X-ray has a wavelength of 0.154 nm (the Cu Kα line used in crystallography). ν = 3.00 × 108 / 0.154 × 10−9 = 1.95 × 1018 Hz. The same radiation has a wavelength of 1.54 Å.
Example 5: time for light to travel
Sunlight takes t = d / c = 1.50 × 1011 m / 3.00 × 108 m/s = 500 s, or about 8.3 minutes, to travel from the Sun to the Earth. Light travels 3.00 × 108 m/s × 3.156 × 107 s = 9.46 × 1015 m in a year, which is a light-year.
Why does chemistry use electromagnetic radiation?
Molecules and atoms absorb and emit radiation at particular wavelengths, depending on their structure:
- Radio waves: nuclear magnetic resonance (NMR) detects the spin of nuclei in a magnetic field.
- Microwaves: rotational transitions of molecules.
- Infrared: vibrations of chemical bonds, used to identify functional groups.
- Visible and ultraviolet: electronic transitions, which give colors to compounds and are used in UV–visible spectroscopy and in photosynthesis.
- X-rays: diffraction by crystals gives the positions of atoms.
How were electromagnetic waves discovered?
James Clerk Maxwell showed in 1865 that his equations for electricity and magnetism predict waves of electric and magnetic fields that travel at a speed that equals the measured speed of light, and he concluded that light is an electromagnetic wave. Heinrich Hertz produced and detected radio waves in the laboratory in 1887–1888, and the unit of frequency is named after him. Wilhelm Röntgen discovered X-rays in 1895, and Paul Villard identified gamma rays in 1900. Infrared radiation had been discovered by William Herschel in 1800, and ultraviolet by Johann Ritter in 1801.
Which mistakes are common?
- Using nanometers in c = λν: convert to meters.
- Mixing up wavelength and frequency: they are inversely proportional.
- Saying that light needs a medium: it travels through a vacuum.
- Treating microwaves and radio waves as different phenomena: they differ only in wavelength.
- Forgetting that the speed changes in a medium: the frequency stays the same, but the wavelength becomes shorter.