Question

How to determine the wavelength and frequency of electromagnetic radiation?

Answer 1

Electromagnetic radiation is made up of waves that are composed of photons which travel at the speed of light, `c`, in a vacuum, which is exactly 299,792,458 m/s, usually rounded to three significant figures as `"3.00"` x `"10"^(8)"m/s"`. Ask your instructor for his or her preference. All electromagnetic waves have wavelength and frequency.

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The wavelength is the distance between two crests, and is measured in length units, such as nanometers, centimeters, or meters. Wavelength is represented by the Greek lowercase letter lambda, `lambda`. Frequency is the number of crests that pass a given point within one second. One wave—or cycle—per second is called a Hertz (Hz). 1 Hz = 1/s or `"s"^(-1)`. Frequency is represented by the Greek lowercase letter nu, `nu`.

For any given photon of electromagnetic radiation, the wavelength times the frequency equals the speed of light: `c` = `lambda` `nu`.

Example Problems

Problem 1. A photon of red light has a wavelength of `"4.50"` x `"10"^(-7)"m"`. Calculate its frequency.

Known/Given:
speed of light, `c` = `"3.00"` x `"10"^8"m/s"`
wavelength, `lambda` = `"4.50"` x `"10"^(-7)"m"`

Equation:
`c` = `lambda` `nu`

Solution:
To solve for frequency, rearrange the equation so that
`nu` = `c`/`lambda`.
`nu` = (`"3.00"` x `"10"^8"m/s"`)`/`(`"4.50"` x `"10"^(-7)"m"`) = `"6.67"` x `"10"^14"/s"` = `"6.67"` x `"10"^14"Hz"`

The frequency of a photon of red light with wavelength `"4.50"` x `"10"^(-7)"m"` is `"6.67"` x `"10"^14"Hz"`.

Problem 2. A photon of green light has a frequency, `nu` of `"5.75"` x `"10"^14"Hz"`. What is its wavelength, `lambda`?

Known/Given:
speed of light, `c` = `"3.00"` x `"10"^8"m/s"`
frequency, `nu` = `"5.75"` x `"10"^14"Hz"` = `"5.75"` x `"10"^14"/s"`

Equation:
`c` = `lambda` `nu`

Solution:
To solve for wavelength, `lambda`, rearrange the equation so that
`lambda` = `c`/`nu`.
`lambda` = (`"3.00"` x `"10"^8"m/s"`)`/`(`"5.75"` x `"10"^14"/s"`) = `"5.22"` x `"10"^(-7)"m"`

The wavelength of a photon of green light with frequency
`"5.75"` x `"10"^14"Hz"` is `"5.22"` x `"10"^(-7)"m"`.