Question

Consider a parallel beam of light of wavelength 600 nm and intensity 100 $W/m^2$. How many photons cross 1 $m^2$ area perpendicular to beam in one second?

• A. $3\times {10}^{16}$
• B. $3\times {10}^{14}$
• C. $3\times {10}^9$
• D. $3\times {10}^4$

Answer 1

Answer: (A)

$3\times {10}^{16}$

The energy of each photon, $E=h\frac{c}{\lambda }$

$=\frac{4.14\times {10}^{-15}\times 3\times {10}^8\times {10}^{-9}}{600}=2.07eV$

Intensity $=100W/m^2$

Power $=$ Intensity $\times$ Area $=100\times \frac{1}{100}\times \frac{1}{100}=0.01J$

Time $=1sec$

Therefore,

Energy $=0.01J$

Number of photons $=\frac{Energyofallphotons}{Energyofonephoton}=\frac{0.01J}{2.07\times {10}^{-19}}\times 1.6=3\times {10}^{16}$