Question #ef851

All you have to do here is to use the wavelength and the frequency of a photon have an inverse relationship as described by the equation

#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)#

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Rearrange the equation to solve for #lamda#

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

Now, before plugging in the value you have for the frequency of the photon, take a look at the units you have for the speed of light and for the frequency.

As you can see, the speed of light is used in meters per second and the frequency is given in hertz, #"Hz"#. The trick here is to use the fact that

#"1 Hz" = "1 s"^(-1)#

to rewrite the frequency of the photon as

#nu = 3.85 * 10^(14)# #"s"^(-1)#

You can now plug in the value to find the wavelength of the photon.

#lamda = (3 * 10^8color(white)(.)"m" color(red)(cancel(color(black)("s"^(-1)))))/(3.85 * 10^(14)color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)(7.79 * 10^(-7)color(white)(.)"m")))#

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