Question

radar guns operate in the microwave region at 22.245 GHz, find the wavelength in nm and angstroms of this radiation.

Answer 1

The speed of a wave is related to the product of its frequency and its wavelength, such that \[v=f\lambda\]. Radar guns use microwave radiation, and hence the speed of of the wave is that of the speed of light \(c=3\times10^8\) m/s.

Recalling that 1 GHz is \(1x10^9\) Hz, the wavelength can be found by \[\lambda=\frac{c}{f}=\frac{3\times10^8}{22.245\times10^9}=0.0135\].

This answer is in metres, but to convert into nanometers and angstroms, we recall that 1 nm = \(1\times10^{-9}\) m and 1 A = \(1\times10^{-10}\). Hence the wavelength is \(1.35\times10^{7}\) nm or \(1.35\times10^{8}\) Angstroms.