A 2 m W laser operates at a wavelength of 500 nm.

Question:

A $2 \mathrm{~mW}$ laser operates at a wavelength of $500 \mathrm{~nm}$. 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 $c=3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$ ]

  1. (1) $5 \times 10^{15}$

  2. (2) $1.5 \times 10^{16}$

  3. (3) $2 \times 10^{16}$

  4. (4) $1 \times 10^{16}$


Correct Option: 1,

Solution:

(1) Energy of photon (E) is given by

$E=\frac{h c}{\lambda}$

Number of photons of wavelength $\lambda$ emitted in $t$ second from laser of power $P$ is given by

$n=\frac{P t \lambda}{h c}$

$\Rightarrow n=\frac{2 \times \lambda}{h c}=\frac{2 \times 10^{-3} \times 5 \times 10^{-7}}{2 \times 10^{-25}}(\because t=1 \mathrm{~S})$

$\Rightarrow n=5 \times 10^{15}$

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