Question

What is the frequency of an x-ray with a wave length of 1nm?

Answer 1

`3 * 10^17 Hz`

Explanation:

an X-ray is on the spectrum of EM (electromagnetic) waves.

all EM waves have a speed of `300,000,000` metres per second, or `3 * 10^8 m//s`.

the equation relating wave speed, frequency and wavelength is

`s = flambda`

where `s` is speed in `m//s`,

`f` is frequency in hertz `Hz`,

and `lambda` is wavelength in metres `m`.

if `s = f * lambda`, then `f = s / lambda`

frequency = speed / wavelength

here, the wavelength is given as `1nm`.

`1` nanometre is the same as `1 * 10-9` metres.

`lambda = 1 * 10^-9 m`

`f = s/lambda = (3 * 10^8)/(1 * 10^-9)`

`3/1 = 3`

`10^8/10^-9 = 10^(8-(-9)`

`= 10^(8+9) = 10^17`

`(3 * 10^8)/(1 * 10^-9) = 3 * 10^17`

the frequency of the EM X-ray, therefore, is `3 * 10^17 Hz`.