Question

What is the wavelength of a $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{}\mathit{m}\mathit{W}$Iaser from which $\mathbf{"}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{15}}$ photons emanate every second?

Short answer

The wavelength of a $2.0mW$Iaser from which $6\times {10}^{15}$ photons emanate every second is $6.00nm$.

Step-by-step solution

Step 1:

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,

$P=\frac{nhc}{\lambda t}$

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

Consider the given data as below.

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

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

Plank’s constant, $h=6.636\times {10}^{-34}J\cdot s$

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

On rearranging equation (1).

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

Substitute known values in the above equation.

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

On converting into nanometres,

$$\begin{gathered} \lambda =\left(5.967\times {10}^{-7}\mathrm{m}\right)\left(\frac{1\times {10}^{-7}\mathrm{m}}{1\mathrm{nm}}\right) \\ =5.967nm \\ \simeq 600nm \end{gathered}$$

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