Question

What is the frequency of a photon that has a wavelength of `"673.8 mm"` ?

Answer 1

`4.452 * 10^(14)` `"s"^(-1)`

Explanation:

The thing to remember about the frequency and the wavelength of a photon is that if you multiply them, you always end up with the speed of light in the medium in which the photon is traveling.

In other words, frequency and wavelength have an inverse relationship that can be described by the following equation

`color(blue)(ul(color(black)(lamda * nu = c)))`

Here

• `lamda` is the wavelength of the photon
• `nu` is its frequency
• `c` is the speed of light in a vacuum, usually given as `3 * 10^(8)` `"m s"^(-1)`

Note that if the problem doesn't specify the medium in which the photon is traveling, you can use the speed of light in a vacuum. Also, keep in mind that the wavelength of the photon must be expressed in meters in order for the frequency of the photon to come out in `"s"^(-1)`.

In order to convert the wavelength from nanometers to meters, you must use the fact that

`color(blue)(ul(color(black)("1 m" = 10^9color(white)(.)"nm")))`

So, rearrange the equation to solve for `nu`

`lamda * nu = c implies nu = c/(lamda)`

Plug in your values to find

`nu = (3 * 10^8color(white)(.)color(blue)(cancel(color(black)("m"))) "s"^(-1))/(673.8 color(red)(cancel(color(black)("nm"))) * (1color(blue)(cancel(color(black)("m"))))/(10^9color(red)(cancel(color(black)("nm")))))`

`nu = color(darkgreen)(ul(color(black)(4.452 * 10^(14)color(white)(.)"s"^(-1))))`

The answer is rounded to four sig figs, the number of sig figs you have for the wavelength of the photon.