Question

Determine the number of photons emitted by the laser each second.
(A) $3.18 \times {10^{15}}$
(B) $4.5 \times {10^{16}}$
(C) $1.2 \times {10^{15}}$
(D) $2.9 \times {10^{17}}$

Answer 1

Photons always travel discreetly in packets. One photon has the energy $h\nu$. The energy is always in the integral multiple of $h\nu$. Find the ratio of the total energy to the energy of one photon to solve this question.

Formula Used: $E = nhv$
where,
$E$ is energy
$n$ is number of photons
$h = 6.62 \times {10^{ - 34}}Js$
$n.v$ should have units of photons second

Complete step by step answer:
We know energy of each photons is given by
$E = \dfrac{{hc}}{\lambda }$
Let $n$ is the no. of photons. Total energy by n photons is
$\Rightarrow nE = \dfrac{{nhc}}{\lambda }$
We know that power is the energy required per unit time to perform some action. i.e.
$P = \dfrac{E}{T}$
Where,
$P$ is power
$E$ is energy
$T$ is time
By substituting the value of $E$ in the above formula, we get
$P = \dfrac{{nhc}}{{\lambda t}}$
$\Rightarrow P = \dfrac{n}{t} \times \dfrac{{hc}}{\lambda }$
Therefore, we can say that, power is equal to the product of number of photons emitted per second and energy of each photon
The energy of photons is

$$\begin{aligned} E &= \dfrac{{hc}}{\lambda } \\\ \Rightarrow &\dfrac{{(6.62 \times {{10}^{ - 34}})(5 \times {{10}^8})}}{{632.8 \times {{10}^{ - 9}}}} \\\ \Rightarrow &3.14 \times {10^{ - 9}}J \\\ \end{aligned}$$

We know that, energy emitted per second by a laser, ${E_l}$ is $5mW$
$\Rightarrow {E_l} = 5 \times {10^{ - 3}}J$
Thus, the no. of photons emitted per second is
$n = \dfrac{{{E_l}}}{E}$
By substituting the value of ${E_l}$ and $E$, we get

$$\begin{aligned} n &= \dfrac{{{E_l}}}{E} \\\ \Rightarrow &\dfrac{{5 \times {{10}^{ - 3}}}}{{3.14 \times {{10}^{ - 19}}}} \\\ \Rightarrow &1.6 \times {10^{16}} \\\ \end{aligned}$$

Additional information:
According to the equation $E = n.h.v$ (Energy $=$ number of photons times Planck’s constant times the frequency)
You divide by Planck’s constant you should get photons per second
$\dfrac{E}{h} = n.v$

Note: To solve this question, you have to keep in mind the law of quantization of energy which says that the energy is always produced in the integral multiple of energy of each photon. Energy of lasers is the total energy produced by all the photons that a laser emits.