Question

An x-ray has a wavelength of 5 nanometers (`5.0 * 10^-9` m). What is the frequency of these x-rays?

Answer 1

The only relationship you need to know here is:

`\mathbf(c/lambda = nu)`

where `c` is the speed of light, `lambda` is the wavelength, and `nu` is the frequency.

You can derive this by simply knowing that the units are:

`"?"/("m") = 1/"s"`

`=> "?" = "m"/"s"`

and evidently, the speed of light is in `"m/s"`. So...

`nu = c/lambda`

`= (2.998xx10^8 cancel"m""/s")/(5.0 xx 10^(-9) cancel"m")`

`= color(blue)(5.996xx10^16 "s"^(-1))` or `color(blue)("Hz")`

A typical X-ray has a frequency of about `3xx10^16` to `3xx10^19 "Hz"`, so this is relatively strong for an X-ray (the lower frequency corresponds to the higher wavelength).