First slide

Quantum Theory of Light

Question

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

Moderate

A

$6 x 10^{20}$
B

$3 x 10^{19}$
C

$1.5 x 10^{20}$
D

$6 x 10^{18}$

Solution

$e f f e c t i v e p o w e r = \frac{25}{100} x 200 = 50 W 50 = \frac{n h c}{λ} n = \frac{50 x 6.6 x 10^{- 34} x 3 x 10^{8}}{6 x 10^{- 7}} = 1.5 x 10^{20}$

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