91Ó°ÊÓ

The given data is listed below as-

The wavelength of light is$\mathrm{λ}=2.40 \mathrm{pm}$

The momentum of a photon is related to its energy and is given by-

$p=\frac{E}{c}$

Here, E is the rest energy of a photon which is given by $E=m_e{c}^2$.

$m_e$ is the mass of the electron and c is the speed of light.

The momentum of a photon is given by-

$p=\frac{E}{c}$

Here, E is the rest energy of electron which is given as

Now,

Substitute for, and in the above equation.

The wavelength of radiation is given by-

$\mathrm{λ}=\frac{h}{p}$

Here, h is the Planck’s constant and p is the momentum.

Substitute for, $h=6.63×{10}^{-34}\mathrm{Js}$and $p=2.73×{10}^{-22}kg.m/s$in the above equation.

Therefore, wavelength is given by-

$$\begin{gathered} p=2.73×{10}^{-22} \\ =\frac{\left({\displaystyle 6.63×{10}^{-34}\mathrm{Js}}\right)}{{\displaystyle 2.73×{10}^{-22}kgm/s}} \\ =2.43\mathrm{pm} \end{gathered}$$

Thus, the wavelength of radiation is 2.43 pm.

The frequency of radiation is given by-

$f=\frac{c}{\mathrm{λ}}$

Here, c is the speed of light and $\mathrm{λ}$is the wavelength.

Substitute for, $c=2.998×{10}^{8}m/s$and $\mathrm{λ}=2.43\mathrm{pm}$in the above equation

Therefore, frequency is obtained as-

$$\begin{gathered} f=\frac{c}{\mathrm{λ}} \\ =\frac{2.998×{10}^{8}m/s}{2.43×{10}^{-12}\mathrm{m}} \\ =1.24×{10}^{20}\mathrm{Hz} \end{gathered}$$

Thus, the frequency of radiation is $1.24×{10}^{20}\mathrm{Hz}.$