A monochromatic source emitting light of wavelength 600 nm has a power output of 66 W. The number of photons emitted by the source in 2 minutes is : (Given: \( h = 6.6 \times 10^{-34}\,\mathrm{J\,s} \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2.4 \times 10^{22} \)
The energy radiated in time \( t \) is \( P\,t \), and each photon carries \( E = hc/\lambda \). So the number of photons is the total energy divided by the energy of one photon.
\( \displaystyle N = \frac{P\,t}{hc/\lambda} = \frac{P\,t\,\lambda}{h c} \)
\( t = 2\,\mathrm{min} = 120\,\mathrm{s} \)
\( \lambda = 600\,\mathrm{nm} = 6\times10^{-7}\,\mathrm{m} \)
\( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle N = \frac{66 \times 120 \times 6\times10^{-7}}{6.6\times10^{-34} \times 3\times10^{8}} \)
\( \displaystyle N = \frac{4.752\times10^{-3}}{1.98\times10^{-25}} = 2.4\times10^{22} \)