Determine the frequency of light with a wavelength of #2.775 * 10^(−7)# #"cm"#. Answer in units of #"Hz"#?

1 Answer
Nov 5, 2017

#1.08 * 10^(17)# #"Hz"#

Explanation:

Your tool of choice here will be the equation that establishes a relationship between the wavelength of the photon, #lamda#, its frequency, #nu#, and the speed of light in a vacuum, #c#.

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

More often than not, the speed of light in a vacuum is given as #3 * 10^8# #"m s"^(-1)#.

Now, notice that the wavelength of the photon is given to you in centimeters, #"cm"#. In order to be able to use it in the equation, you need to convert it to meters, #"m"#.

#"1 m" = 10^3# #"m"#

You will have

#overbrace(2.775 * 10^(-7)color(white)(.)"cm")^(color(blue)(lamdacolor(white)(.)"in cm")) = 2.775 * 10^(-7) color(red)(cancel(color(black)("cm"))) * "1 m"/(10^2color(red)(cancel(color(black)("cm")))) = overbrace(2.775 * 10^(-9)color(white)(.)"m")^(color(blue)(lamda color(white)(.)"in m"))#

Next, rearrange the equation to solve for the frequency of the photon

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

Plug in your value to find

#nu = (3 * 10^8 color(red)(cancel(color(black)("m"))) "s"^(-1))/(2.775 * 10^(-9)color(red)(cancel(color(black)("m")))) = 1.08 * 10^(17)color(white)(.)"s"^(-1)#

Finally, to express the frequency in hertz, use the fact that

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

You will have

#nu = color(darkgreen)(ul(color(black)(1.08 * 10^(17)color(white)(.)"Hz")))#

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