Rankers Physics

Photoelectric Effects and deBroglie Equation: Practice Problem & Solution

13. 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. (2012 Pre)
$1.5 \times 10^{20}$
$6 \times 10^{18}$
$62 \times 10^{29}$
$3 \times 10^{19}$

Solution Explained:

To solve this problem, we apply the core principles of Photoelectric Effects and deBroglie Equation. Understanding the underlying formula is key to arriving at the correct answer below:

Useful power for light emission is $P = 25\% \text{ of } 200 W = 50 W$. The energy of one photon is $E = \frac{hc}{\lambda} = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{0.6 \times 10^{-6}} = 3.3 \times 10^{-19} J$. The number of photons emitted per second is $n = \frac{P}{E} = \frac{50}{3.3 \times 10^{-19}} \approx 1.5 \times 10^{20}$.

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