The number of photons emitted per minute by a 25 W source of monochromatic light of wavelength 6000 Å is approximately: (take \( h = 6.6 \times 10^{-34}\,\mathrm{J\,s} \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 4.5 \times 10^{21} \)
The number of photons is the energy radiated divided by the energy of one photon, \( E = hc/\lambda \).
\( \lambda = 6000\,\mathring{\mathrm{A}} = 6000\times10^{-10}\,\mathrm{m} = 6\times10^{-7}\,\mathrm{m} \)
\( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle E = \frac{hc}{\lambda} = \frac{6.6\times10^{-34} \times 3\times10^{8}}{6\times10^{-7}}\,\mathrm{J} = 3.3\times10^{-19}\,\mathrm{J} \)
Energy radiated in one minute:
\( P\,t = 25\,\mathrm{W} \times 60\,\mathrm{s} = 1500\,\mathrm{J} \)
\( \displaystyle N = \frac{P\,t}{E} = \frac{1500}{3.3\times10^{-19}} = 4.5\times10^{21} \)