How many photons are produced in a laser pulse of 0.188 J at 571 nm?

Friday, October 10, 2014

How many photons are produced in a laser pulse of 0.188 J at 571 nm?

A photon of frequency f has the energy E = hf, where h is the Planck's constant:

$\displaystyle{h}={6.63}\cdot{{10}}^{{-{34}}}{J}\cdot{s}$ .

The frequency is related to the wavelength as $\displaystyle{f{=}}\frac{{c}}{\lambda}$ , where c is the speed of light: $\displaystyle{c}={3}\cdot{{10}}^{{8}}\frac{{m}}{{{s}}^{{2}}}$ . So the photons in the laser pulse with the wavelength of 571 nm have frequency

$\displaystyle{f{=}}\frac{{c}}{\lambda}=\frac{{{3}\cdot{{10}}^{{8}}}}{{{571}\cdot{{10}}^{{-{9}}}}}={5.25}\cdot{{10}}^{{14}}{{s}}^{{-{1}}}$ .

Each of these photons then have the energy of $\displaystyle{E}={h}{f{=}}{6.63}\cdot{{10}}^{{-{34}}}\cdot{5.25}\cdot{{10}}^{{14}}={34.8}\cdot{{10}}^{{-{20}}}{J}={3.48}\cdot{{10}}^{{-{19}}}{J}$ .

So, if the total energy of the pulse is 0.188 J, this pulse contains the number of photons equal to the total energy divided by the energy of a single photon:

$\displaystyle\frac{{0.188}}{{{3.48}\cdot{{10}}^{{-{19}}}}}={0.054}\cdot{{10}}^{{19}}={54}\cdot{{10}}^{{16}}$ photons.

The laser pulse of the given energy and wavelength contains

540,000,000,000,000,000 photons.

Blog

Friday, October 10, 2014