Question

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

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

Answer 1

The correct option is A

$5\times {10}^{15}$

Step 1: Given Data

Power of the laser $P=2mW=2\times {10}^{-3}W$

The wavelength of the laser $\lambda =500nm=5\times {10}^{-7}m$

Planck's constant $h=6.6\times {10}^{-34}Js$

Speed of light $c=3.0\times {10}^{8}m/s$

Time given $t=1s$

Step 2: Establish the Formula

We know that energy is given as,

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

Power is given as,

$P=\frac{E}{t}$

$\therefore P=\frac{nhc}{\lambda t}$

$\Rightarrow n=\frac{P\lambda t}{hc}$

Step 3: Calculate number of Photons

Upon substituting the values we get,

$n=\frac{2\times {10}^{-3}\times 5\times {10}^{-7}\times 1}{6.6\times {10}^{-34}\times 3\times {10}^8}$

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

Hence, the correct answer is option (A).