Question

A Laser light of wavelength $600nm$ is used to weld retinal detachment. If a Laser pulse of width $60ms$ and $0.5kW$ is used, the approximate number of photons in the pulse are:
Take planck's constant $h = 6.62 \times {10^{ - 4}}Js$
A. ${10^{20}}$
B. ${10^{18}}$
C. ${10^{22}}$
D. ${10^{19}}$

Answer 1

This question is about the particle part of light which is believed to be a wave, thermionic emission which involves emission of light particles as a result of heat or radiant heat that strikes the surface of a plate.

Complete step by step answer:
We are given a Laser light of wavelength $600nm$ is used to weld retinal detachment and the width of the Laser pulse is $60ms$ and power is $0.5kW$.
We have to find the approximate no. of photos present in the pulse.
Photons are the particles which get emitted when light strikes a metal surface.
We need to first generate the formula that connects energy, number of photons and time, thereafter connect the parameters together.
Energy from the laser = $\dfrac{{hc}}{\lambda }$
The ratio of change in number of photon with time or pulse = $\dfrac{{\Delta n}}{{\Delta t}}$
The wavelength is in nanometer which is converted to practical unit meter which is ${10^{ - 9}}m$, the pulse is also converted to practical unit seconds ${10^{ - 3}}s$.
So the Power generated = $\dfrac{{\Delta n}}{{\Delta t}} \times \dfrac{{hc}}{\lambda }$
$0.5 \times {10^3} = \dfrac{{\Delta n}}{{60 \times {{10}^{ - 3}}}} \times \dfrac{{6.62 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{660 \times {{10}^{ - 9}}}}$
We would then cross multiply and make $\Delta n$ the subject of the relation or formula.
$\Delta n = \dfrac{{0.5 \times {{10}^3} \times 60 \times {{10}^{ - 3}} \times 660 \times {{10}^{ - 9}}}}{{6.62 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}} \\\ \to \Delta n = 996.97 \times {10^{17}} \\\$
We can also move the decimal point three steps to the left hand side, where the answer will now look like
$\Delta n = 0.99 \times {10^{20}} \\\ \Delta n \simeq {10^{20}} \\\$
So the right option for this question is Option A, ${10^{20}}$
The number of photons in the pulse is approximately equal to ten raised to the power of 20.

Note: This again is applied in other light packed properties where the radiation of light on some surfaces is important, phenomena like photoelectric emission which involves the liberation of photons or quanta of light.