Question

How many photons are emitted per second by a $5mW$ laser source operating at $632.8nm$?

Answer 1

Step 1: Given data

Power : $5mW=5\times {10}^{-3}W$

We know that the unit of energy is equal to the product between the unit of power and time.

$\therefore$ $J=W\times s$

$\therefore$Energy of laser per second $=\frac{5\times {10}^{-3}}{1}=5\times {10}^{-3}J$

The wavelength of laser source :$632.8nm$

Step 2: Calculate the energy of each photon

We know that the energy of a particle is given as

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

Where $h=6.62\times {10}^{-34}Js$ is the Planck's constant, $c=3\times {10}^{8}m/s$ is the speed of light, and $\lambda =632.8nm$ is the given wavelength.

Upon substituting these values we get,

$E=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{632.8\times {10}^{-9}}$

$=0.0314\times {10}^{\left(-34+8+9\right)}$

$=3.14\times {10}^{-19}J$

Step 3: Calculate the number of photons

Given that the total energy of the laser source is$=5\times {10}^{-3}J$

Therefore, the total number of photons,

$=\frac{totalenergyoflaser}{energyofeachphoton}$

$=\frac{5\times {10}^{-3}}{3.14\times {10}^{-19}}$

$=1.6\times {10}^{16}$ photons

Hence, $1.6\times {10}^{16}$ number of photons is emitted through this laser each second.