A 2 mW laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is [Given Planck's constant $\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}$, speed of light $\mathrm{c}=3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$]

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Modern Physics

A 2 mW laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is
[Given Planck's constant

h = 6.6 \times 1 0^{- 34} Js

, speed of light

c = 3.0 \times 1 0^{8} m / s

]

(A) $1 \times 1 0^{16}$
(B) $1.5 \times 1 0^{16}$
(C) $2 \times 1 0^{16}$
(D) $5 \times 1 0^{15}$ ✓ Correct

Answer: (D)

Solution

Each photon of this light carries energy

E = \frac{h c}{λ}

, and the laser's power is just this energy times the number emitted per second,

P = \frac{h c}{λ} \frac{d n}{d t}

. Solving for the rate,

\frac{d n}{d t} = \frac{P λ}{h c} = \frac{( 2 \times 1 0 ^{- 3} ) ( 500 \times 1 0 ^{- 9} )}{( 6.6 \times 1 0 ^{- 34} ) ( 3 \times 1 0 ^{8} )} \approx 5 \times 1 0^{15}

photons every second.

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option

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