Question:

A $200\, W$ sodium street lamp emits yellow light of wavelength $0.6 \, \mu m. $ Assuming it to be $25 \% $ efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is

Updated On: Jul 1, 2024
  • $1.5 \times 10^{20} $
  • $6 \times 10^{18} $
  • $62 \times 10^{20} $
  • $3 \times 10^{19} $
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The Correct Option is A

Solution and Explanation

The number of photons per sec, $n =$ amount of power converted to light / energy of photon
Power converted to light $P _{1}=200(25 / 100)=50 W$
Energy of photon, $E _{ p }=\frac{ hc }{\lambda}=\frac{6.62 \times 10^{-34} \times 3 \times 10^{8}}{0.6 \times 10^{-6}}=33.1 \times 10^{-20} J$
Thus, $n =\frac{50}{33.1 \times 10^{20}}=1.5 \times 10^{20}$
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