Question

What is the wavelength of a photon that has a frequency of `"89 MHz"` ?

Answer 1

`"3.4 m"`

Explanation:

All you have to do here is to use the fact that wavelength and frequency have an inverse relationship described by the 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)`

Now, notice that the frequency of the photons is given to you in megahertz, As you know, you have

`"1 Hz" = "1 s"^(-1)" "` and `" " "1 MHz" = 10^6color(white)(.)"Hz"`

which means that you can rewrite the frequency of the photons as

`"89 MHz" = 89 color(red)(cancel(color(black)("MHz")))* (10^6color(red)(cancel(color(black)("Hz"))))/(1color(red)(cancel(color(black)("MHz")))) * "1 s"^(-1)/(1color(red)(cancel(color(black)("Hz")))) = 8.9 * 10^7color(white)(.)"s"^(-1)`

So, rearrange the equation to solve for the wavelength of each photon

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

Plug in the values to get

`lamda = (3 * 10^8 color(white)(.)"m" color(red)(cancel(color(black)("s"^(-1)))))/(8.9 * 10^7 color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)("3.4 m")))`

The answer is rounded to two sig figs, the number of sig figs you have for the frequency of the photons.