Question

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

• A. $3\times {10}^{10}{s}^{-1}$
• B. $9\times {10}^{13}{s}^{-1}$
• C. $7\times {10}^{20}{s}^{-1}$
• D. $6\times {10}^{19}{s}^{-1}$

Answer 1

The correct option is B $9\times {10}^{13}{s}^{-1}$

$\lambda =3\times {10}^{-7}m,A=4\times {10}^{-4}{m}^2,I=150\times {10}^{-3}W/m^2\therefore I=\frac{E}{A\times t}=\frac{nhc}{\lambda \times At}\Rightarrow \left(\frac{n}{t}\right)=\frac{I\lambda A}{hc}=\frac{150\times {10}^{-3}\times 3\times {10}^{-7}\times 4\times {10}^{-4}}{6.6\times {10}^{-34}\times 3\times {10}^8}=9\times {10}^{13}{s}^{-1}$