Question

What is the frequency of a photon with a wavelength of `2.5 * 10^-9` m? In what region of the spectrum is this located?

Answer 1

The wavelength `2.5xx10^(-9)"m"` is in the soft X-ray region of the electromagnetic spectrum.

The frequency of the `2.5xx10^(-9)"m"` wavelength is `1.2xx10^17"Hz"`.

Explanation:

Photons travel at the speed of light in a vacuum, `3.00xx10^8 "m/s"` rounded to three significant figures. The relationship between speed of light `(c)`, wavelength `(lambda)` (pronounced lambda), and frequency `(nu)` (pronounced noo), is given mathematically as `c=lambda*nu`.

The wavelength `2.5xx10^(-9)"m"` is in the soft X-ray region of the electromagnetic spectrum. `2.5xx10^(-9)"m"="25 Ångströms"`

http://www.britannica.com/science/soft-X-ray

To find the frequency of a photon with a wavelength of `2.5xx10^(-9) "m"`, rearrange the equation to isolate `nu` and solve. The unit for frequency is `"1/s"`, or Herz (Hz).

`nu=(c/lambda)`

`nu=(3.00xx10^8cancel"m"/"s")/(2.5xx10^(-9)cancel"m")=1.2xx10^17"/s"=1.2xx10^17 "Hz"`