Question

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

• A. $2\times {10}^{16}$
• B. $1\times {10}^{16}$
• C. $1.5\times {10}^{16}$
• D. $5\times {10}^{15}$

Answer 1

The correct option is D $5\times {10}^{15}$

Given:
Power of laser $=2\text{mW}$
wavelength $=500\text{nm}$.
Planck's constant $h=6.6\times {10}^{-34}\text{Js}$
speed of light $c=3.0\times {10}^8\text{m/s}$

Energy of photon $\left(E\right)$ is given by

$E=\frac{hc}{\lambda }$

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

$n=\frac{Pt\lambda }{hc}$

$\Rightarrow n=\frac{2\times {10}^{-3}\times 1\times 5\times {10}^{-7}}{6.6\times {10}^{-34}\times 3\times {10}^8}(\because t=1S)$

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

Hence option $\left(A\right)$ is correct.