A 200 W 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

Question

A 200 W 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 (A) 1.5 × 1020  (B) 6 × 1018  (C) 62 × 1020  (D) 3 × 1019

Tardigrade Admin · Accepted Answer

Energy of a photon, =((6.6 × 10-34 J s )(3 × 108 m s -1)/0.6 × 10-6 m ) =33 × 1020 J Number of photons emitted per second is N=((25/E) P/E)=((25/100) × 200 W /33 × 10-20 J )=1.5 × 1020

Q. A $200 W$ 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

$1.5 \times 1 0^{20}$

$6 \times 1 0^{18}$

$62 \times 1 0^{20}$

$3 \times 1 0^{19}$

Energy of a photon,
$= \frac{( 6.6 \times 1 0 ^{- 34} J s ) ( 3 \times 1 0 ^{8} m s ^{- 1} )}{0.6 \times 1 0 ^{- 6} m}$
$= 33 \times 1 0^{20} J$
Number of photons emitted per second is
$N = \frac{\frac{25}{E} P}{E} = \frac{\frac{25}{100} \times 200 W}{33 \times 1 0 ^{- 20} J} = 1.5 \times 1 0^{20}$

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

1.5×1020

6×1018

62×1020

3×1019