Question

Question #fd5ae

Answer 1

`5.9 * 10^(-7)"m"`

Explanation:

The thing to remember about wavelength, `lamda`, and frequency, `nu`, is that they have an inverse relationship as described by the equation

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

Here `c` is the speed of light in a vacuum, usually given as `3 * 10^8"m s"^(-1)`.

This inverse relationship basically means that if you multiply the frequency and the wavelength of a given electromagnetic wave, the result will always be equal to the speed of light.

You can rearrange the equation to solve for `lamda`

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

Now, keep in mind that the frequency of yellow light is given to you in hertz, `"Hz"`, which as you know are equivalent to `"s"^(-1)`.

You will thus have

`lamda = (3 * 10^8"m" color(red)(cancel(color(black)("s"^(-1)))))/(5.1 * 10^(14) color(red)(cancel(color(black)("s"^(-1))))) = color(darkgreen)(ul(color(black)(5.9 * 10^(-7)"m")))`

The answer is rounded to two sig figs because the speed of light is a constant, which implies that you can use it with as many significant figures as you want.