Question

How do you determine the frequency of light whose wavelength is `4.257 x 10^-7` cm?

Answer 1

Please see the explanation.

Explanation:

Let `c = "the speed of light" = 3.0 xx 10^8 m/s`
Let `lambda = "the wavelength" = 4.257 xx 10^-9 m`
Let `f =` the unknown frequency (in Hz which is the same as `s^-1`).

NOTE: I converted the wavelength from cm to m.

Please observe this equation has consistent units:

`c" (in "m/s) = lambda " (in meters) " xx f " (in Hz or s"^-1")"`

When you divide both sides by `lambda`, the units remain consistent:

`f = c/lambda`

`f = (3.0 xx 10^8 m/s)/(4.257 xx 10^-9m)`

`f = 7.0 xx 10^16 Hz`