Modern Physics 2 Question 2
2. A $2 mW$ laser operates at a wavelength of $500 nm$. 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 $\left.c=3.0 \times 10^{8} m / s\right]$
(a) $1 \times 10^{16}$
(b) $5 \times 10^{15}$
(c) $1.5 \times 10^{16}$
(d) $2 \times 10^{16}$
(Main 2019, 10 April II)
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Answer:
Correct Answer: 2. (b)
Solution:
- Power of laser is given as
$$ \begin{aligned} & P=\frac{\text { Energy }}{\text { Time }} \\ & \text { Number of photons emitted } \times \text { Energy of } \\ & =\ldots \text { one photon } \\ & \text { Time } \\ & \Rightarrow \quad P=\frac{N E}{t}=\frac{N}{t} \cdot E \end{aligned} $$
So, number of photons emitted per second
$$ \begin{aligned} & =\frac{N}{t}=\frac{P}{E} \\ & =\frac{P}{h c / \lambda}=\frac{P \lambda}{h c} \quad \because E=h \nu=\frac{h c}{\lambda} \end{aligned} $$
Here, $h=6.6 \times 10^{-34} J-s, \lambda=500 nm=500 \times 10^{-9} m$
$$ \begin{aligned} c & =3 \times 10^{8} ms^{-1} \\ P & =2 mW=2 \times 10^{-3} W \\ \therefore \quad \frac{N}{t} & =\frac{2 \times 10^{-3} \times 500 \times 10^{-9}}{6.6 \times 10^{-34} \times 3 \times 10^{8}} \\ & =5.56 \times 10^{15} \\ & \approx 5 \times 10^{15} \text { photons per second } \end{aligned} $$
