What is the wavelength of a photon that has a frequency of #"89 MHz"# ?
1 Answer
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.