Question

Monochromatic light of wavelength $3000\dot{\text{A}}$ is incident on a surface area $4{\text{cm}}^2$. If the intensity of light is $150{\text{mW/m}}^2$, then the rate at which photons strike the target is

• A. $9\times {10}^{13}{\text{sec}}^{-1}$
• B. $18\times {10}^{12}{\text{sec}}^{-1}$
• C. $27\times {10}^7{\text{sec}}^{-1}$
• D. $36\times {10}^{13}{\text{sec}}^{-1}$

Answer 1

The correct option is A $9\times {10}^{13}{\text{sec}}^{-1}$

Given,
Area of the surface, $A=4{\text{cm}}^2$,
Intensity of incident light, $I=150{\text{mW/m}}^2$,

Total energy incident on the surface in one second,

$E_T=IA=0.150\times 4\times {10}^{-4}=6\times {10}^{-5}\text{J}$

Energy of incident photon,

$E_p=\frac{hc}{\lambda }=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{3000\times {10}^{-10}}=6.63\times {10}^{-19}\text{J}$

Number of photons,

$N=\frac{E_T}{E_p}=\frac{6\times {10}^{-5}}{6.63\times {10}^{-19}}\approx 9\times {10}^{13}\text{photons/sec}$

Hence, $\left(A\right)$ is the correct answer.