Question

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

• A. $3 \times 10^{10} /\sec $
• B. $9 \times 10^{13} /\sec $
• C. $7 \times 10^{15} /\sec $
• D. $6 \times 10^{19} /\sec $

Answer 1

Answer: (B)

Area of the surface $A =4 \,cm ^{2}=4 \times 10^{-4} \,m ^{2}$
Intensity of incident light $E =150 \,mW / m ^{2}$
Thus total energy incident on the surface
$E_{i}=0.150 \times 4 \times 10^{-4}=6 \times 10^{-5} J$ in one second
Wavelength of photon $\lambda=3000 \times 10^{-10} \,m$
Energy of incident photon
$E_{p}=\frac{h c}{\lambda}=\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{3000 \times 10^{-10}}=6.63 \times 10^{-19}\, J$
Number of photons $N =\frac{ E _{ i }}{ E _{ p }}=\frac{6 \times 10^{-5}}{6.63 \times 10^{-19}}=9 \times 10^{13}$ photons/ second