Question

Monochromatic light of wavelength $632.8nm$ is produced by a Helium-Neon laser. The power emitted is $9.42mW$. How many photons per second, on average, arrive at a target irradiated by this beam?

Answer 1

Step 1: Given Data

Wavelength of monochromatic light: $\lambda =632.8nm=632.8\times {10}^{-9}m$

Power emitted by the laser: $P=9.42mW=9.42\times {10}^{-3}W$

Planck's constant: $h=6.626\times {10}^{-34}Js$

Speed of light: $c=3\times {10}^{8}m/s$

Step 2: Formula Used

The energy of a single photon is given by the formula $E=\frac{hc}{\lambda }$.

The momentum is given by the formula $P=nE$, where $n$ is the number of photons per second and $E$ is energy. Thus, $n=\frac{P}{E}$.

Step 3: Calculate the Number of Photons

Find the energy of each photon using the formula

$\begin{array}{rcl}E& =& \frac{hc}{\lambda }\\ & =& \frac{6.626\times {10}^{-34}\times 3\times {10}^8}{632.8\times {10}^{-9}}J\\ & =& 0.0314\times {10}^{-17}J\\ & =& 3.14\times {10}^{-19}J\end{array}$

Find the number of photons by using the formula.

$\begin{array}{rcl}n& =& \frac{P}{E}\\ & =& \frac{9.42\times {10}^{-3}}{3.14\times {10}^{-19}}photons/sec\\ & =& 3\times {10}^{16}photons/sec\end{array}$

Hence, the number of photons are $3\times {10}^{16}photons/sec$ .