Question

How many photons are produced in a laser pulse of $0.210J$ at $535nm$ ?

Answer 1

Hint: In order to determine the number of photons which are produced in a laser pulse of $0.210J$ at wavelength of $535nm$ , we must use the Planck Einstein equation by which we can get the energy of photon and then use the total energy of laser pulse.

Formula used:
$E = h\nu $
Where, $E$ = Energy of the photons
$h$ = Planck’s constant $(6.626 \times {10^{ - 34}}J\operatorname{s} )$
And $\nu $ = Frequency of the photon

Complete step by step answer:
According to Planck Einstein relation:
Energy of the photon is directly proportional to the frequency of the photon, hence mathematically energy of photon is equal to the product of frequency of photon and planck’s constant.
$E = h\nu $
Where, $E$ = Energy of the photons
$h$ = Planck’s constant $(6.626 \times {10^{ - 34}}J\operatorname{s} )$
And $\nu $ = Frequency of the photon
Now, to calculate the frequency of a photon we have to use the relation between frequency and wavelength. The relation is given as:
$\lambda \nu = c$
Where, $\lambda $ = wavelength of photon
$\nu $ = frequency of photon
And $c$ = Velocity of light in vacuum $(3 \times {10^8}m/s)$
By the above relation we will get:
$ \Rightarrow \nu = \dfrac{c}{\lambda }$
By substituting the values we will get the frequency as:
$\
   \Rightarrow \nu = \dfrac{{3 \times {{10}^8}m{\operatorname{s} ^{ - 1}}}}{{535 \times {{10}^{ - 9}}m}} \\
   \Rightarrow \nu = 5.607 \times {10^{14}}{\operatorname{s} ^{ - 1}} \\
\ $
Now, we can substitute the values in the Planck Einstein relation to determine the energy of the photon. So, by plug in the values we will get:
$\
  E = 6.626 \times {10^{ - 34}}J\operatorname{s} \times 5.607 \times {10^{14}}{\operatorname{s} ^{ - 1}} \\
   \Rightarrow E = 3.716 \times {10^{ - 19}}J \\
\ $
Now, we have to use the total energy of laser pulse to find the total number of photons needed for the output:
$\
  0.210J = \dfrac{{1Photon}}{{3.716 \times {{10}^{ - 19}}J}} \\
   \Rightarrow 5.65 \times {10^{17}}Photons \\
\ $
Hence, $5.65 \times {10^{17}}$ photons are produced in a laser pulse of $0.210J$ at $535nm$ .

Note:
The photon is a type of elementary particle. It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum.