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?

1 Answer
Meave60
Dec 1, 2015

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"#

![http://www.dreamstime.com/stock-photos-electromagnetic-spectrum-all-possible-frequencies-radiation-colors-visible-image31930793](useruploads.socratic.org)

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