Question

If `nu=2.61xx10^-9*s^-1`, what is the wavelength of this light?

Answer 1

`lambda = 1.15 xx 10^8` `"nm"`

Explanation:

The relationship between the wavelength `lambda` and he frequency `f` of a particle is

`lambdaf = c`

Where `c` is the speed of light in vacuum, equal to precisely `299,792,458` `"m/s"`.

Recall that `1` `"Hz"` is the same as `1` `"s"^(-1)`, so the given frequency is also equal to `2.61xx10^9` `"s"^(-1)`.

Let's now plug in the known values and solve for the wavelength:

`lambda = c/f = (299792458color(white)(l)"m/"cancel("s"))/(2.61xx10^9color(white)(l)cancel("s"^(-1))) = color(red)(0.115` `color(red)("m"`

This value in nanometers is

`color(red)(0.115)cancel(color(red)("m"))((10^9color(white)(l)"nm")/(1cancel("m"))) = color(blue)(1.15 xx 10^8` `color(blue)("nm"`

Answer 2

Well, `c=nuxxlambda`, where `c="speed of light,"` `m*s^-1`.

Explanation:

..........`nu="frequency, "s^-1`. And `lambda="wavelength"`, whose units are `m`.

And of course, `c=3.00xx10^8*m*s^-1`

And thus the product, `nuxxlambda` has units `m*s^-1` as is required for a velocity/speed.

And so `lambda=c/nu` `=` `(3.00xx10^8*m*s^-1)/(2.61xx10^9*s^-1)`

`=0.115*m`.

This is an exceptionally long wavelength.