91Ó°ÊÓ

Each photon's energy is inversely proportional to the light's frequency. A light beam also has the potential to include any number of photons, which contributes to its total power. The amount of energy a beam transmits in a given amount of time is its power.

The power of the photon is,

$P=\frac{nhc}{\mathrm{λ}t}$

Here, $P$ is the power, $n$ is the number of photons, $h$ is the plank’s constant, $c$is the speed of light, $\mathrm{λ}$is the wavelength, and $t$is the time.

Consider the given data as below.

The power, $P=2mW=0.002W$

The number of electrons, $n=6×{10}^{15}electrons$

Plank’s constant, $h=6.636×{10}^{-34}Jâ‹\dots s$

Speed of light, $c=3×{10}^8\frac{m}{s}$

On rearranging equation (1).

localid="1657553432021" $\mathrm{λ}=\frac{\mathrm{nhc}}{\mathrm{Pt}}$

Substitute known values in the above equation.

localid="1657553527687" $$\begin{gathered} \mathrm{λ}=\frac{\mathrm{nhc}}{\mathrm{Pt}} \\ =\frac{6×{10}^{15}×6.636×{10}^{-34}×3×{10}^8.}{0.002×1} \\ =5.967×{10}^{-7}\mathrm{m} \end{gathered}$$

On converting into nanometres,

$$\begin{gathered} \mathrm{λ}=\left(5.967×{10}^{-7}\mathrm{m}\right)\left(\frac{1×{10}^{-7}\mathrm{m}}{1\mathrm{nm}}\right) \\ =5.967nm \\ ≃600nm \end{gathered}$$

Hence, the wavelength of light that produces if is $600nm$.