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

May 23, 2015

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

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

#### Explanation:

Practice Problem

What is the frequency of the wavelength of light of $650 \text{nm}$?

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

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 $\nu$.

$\nu = \frac{c}{\lambda}$

$\left(3.00 \times {10}^{8} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{m"))/"s")/(6.50xx10^(-7)color(red)cancel(color(black)("m}}}}\right)$ =

$\frac{4.62 \times {10}^{14}}{s} = 4.62 \times {10}^{14}$ $\text{Hz}$

Hertz (Hz) is the unit for frequency. It is $\frac{1}{\text{s}}$ .