Question

Police often monitor traffic with "K-band" radar guns, which operate in the microwave region at 22.235 GHz (1 GHz = 109 Hz). Find the wavelength (in nm and Å) of this radiation. Enter your answers in scientific notation.

Answer 1

Answer: The wavelength is $0.013\times 10^{9}nm$ and $0.013\times 10^{10}A^0$ of this radiation

Explanation:

To calculate the wavelength of light, we use the equation:

$\lambda=\frac{c}{\nu}$

where,

$\lambda$ = wavelength of the light  = ?

c = speed of light = $3\times 10^8m/s$

$\nu$ = frequency of light = $22.235GHz=22.235\times 10^{9}Hz=22.235\times 10^{9}s^{-1}$

$\lambda=\frac{3\times 10^8m/s}{22.235\times 10^9s^{-1}}=0.013m$

$\lambda=0.013m=0.013\times 10^{9}nm$     $1m=10^{9}nm$

$\lambda=0.013m=0.013\times 10^{10}A^0$      $1m=10^{10}A^0$

Thus wavelength is $0.013\times 10^{9}nm$ and $0.013\times 10^{10}A^0$ of this radiation