Question

A laser pulse with wavelength 525 nm contains 4.40 mj of energy. How many photons are in the laser pulse

Answer 1

The laser pulse in this question has a wavelength of $\lambda=524 nm=525\times 10^{-9}m$. To solve this problem, we first have to calculate the energy of a single photon in the laser pulse. The equation for calculating the energy of a single photon of an electromagnetic wave is $E=\frac{hc}{\lambda}$ where $c$ is the speed of light, $h$ is planks constant and $\lambda$ is the wave length of the photons.

For this problem, $c=3.0\times 10^8m/s$, $h=6.63\times10^{-34}J.s$ and $\lambda=525\times 10^{-9}m$. We use these values to calculate the energy of the photon as shown below,

$E=\frac{hc}{\lambda} \\E=\frac{(6.63\times 10^{32}Js)\times(3.0\times10^8m/s)}{525\times 10^{-9}m} \\E=3.79\times 10 ^{-19}J.$

Now that we know the energy for a single photon, we will divide the total energy given by the energy of one photon to get the number of photons in the pulse. The number of photons $n$ is calculated as shown below,

$n=\frac{4.4\times 10^{-3}J}{3.79\times10^{-19}J} =1.16\times 10^{16}$. There are $1.16\times 10^{16}$ photons.