Question

A laser light of wavelength $600nm$ is used to weld Retinal detachment. If a laser pulse of width $60ms$ and power $0.5KW$ is used, the approximate number of photons in the pulse is:
[Take planck's constant $h=6.62\times {{10}^{-34}}Js$]
$\text{A}\text{. }{{10}^{20}}$
$\text{B}\text{. }{{10}^{18}}$
$\text{C}\text{. }{{10}^{22}}$
$\text{D}\text{. }{{10}^{19}}$

Answer 1

Hint: We can calculate the number of photons in the laser pulse using the formula of power of laser light. We will need the value of wavelength of pulse, speed of light, Planck's constant, power associated with the pulse, and the time being for which the laser light is generated.

Formula used:
$P=\dfrac{nhc}{\lambda t}$

Complete step by step answer:
A laser is an appliance which emits light by the process of optical amplification based on the stimulated emission of electromagnetic radiation. Lasers produce an extremely narrow beam of light that is useful in many technological and instruments. We can say that a laser stimulates atoms or molecules to emit light at particular wavelength and amplifies that light wave, producing a very narrow beam of radiation. The emission usually covers an extremely limited range of visible, infrared, or ultraviolet wavelengths.
Laser emission is framed by the rules of quantum mechanics, which limit atoms and molecules to having discrete amounts of stored energy that depend on the nature of the atom or molecule. When one or even more electrons of an atom have absorbed the energy, they can move to outer orbits, and the atom is referred to as being in an excited state. Excited states are generally not stable. As electrons drop from higher energy level to lower energy level, they emit the extra energy as light.
The power of a laser is defined as the energy delivered by a laser beam per unit time. The unit of power is Watt.
Formula for power of laser light is given as,
$P=\dfrac{nhc}{\lambda t}$
$n$ is the number of photons
$h$ is the planck's constant
$c$ is the speed of light
$\lambda $ is the wavelength
$t$ is the time
We are given, $P=0.5KW=500W$
$\lambda =660nm=660\times {{10}^{-9}}m$
$t=60ms=60\times {{10}^{-3}}\sec $
$h=6.6\times {{10}^{-34}}Js$
$c=3\times {{10}^{8}}m{{s}^{-1}}$
Now,
$P=\dfrac{nhc}{\lambda t}$
$n=\dfrac{P\lambda t}{hc}$
Putting all the given values in the above equation, we get,
$n=\dfrac{500\times 660\times {{10}^{-9}}\times 0.06}{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}$
$n=\left( \dfrac{500\times 100\times 0.06}{3} \right)\times {{10}^{17}}$
$n={{10}^{20}}$
Therefore, number of photons in the pulse is approximately equal to ${{10}^{20}}$
Hence, the correct option is A.

Note: While calculating the number of electrons in the pulse, working in SI units only is recommended to ensure no calculation error. Changing units of some of the terms can develop errors in the final answer obtained.