Question

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

Answer 1

`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.