What is the relationship between the speed of light, wavelength, and frequency of electromagnetic radiation?

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Answer 1 · 2015-05-23T17:27:37

$c = λ \cdot ν$ $c=lambda*nu$ , where $c$ $c$ is the speed of light, $λ$ $lambda$ is the wavelength, and $ν$ $nu$ is the frequency.

The speed of light in a vacuum, $c$ $c$ , is $3.00 \times 10^{8} m/s$ $3.00xx10^(8)"m/s"$ rounded to 3 significant figures.

Practice Problem

What is the frequency of the wavelength of light of $650 nm$ $650"nm"$ ?

( $1 nm$ $"1 nm"$ = $1 \times 10^{- 9}$ $1xx10^(-9)$ $m$ $"m"$ )

Convert wavelength to meters.

$650.0color(red)cancel(color(black)("nm"))xx(1xx10^(-9)"m")/(1color(red)cancel(color(black)("nm")))=6.50xx10^(-7)"m"$

Rearrange the equation to isolate $nu$ .

$nu=c/lambda$

$(3.00xx10^8color(red)cancel(color(black)("m"))/"s")/(6.50xx10^(-7)color(red)cancel(color(black)("m")))$ =

$(4.62xx10^14)/s=4.62xx10^14$ $"Hz"$

Hertz (Hz) is the unit for frequency. It is $1/"s"$ .