Question

A helium-neon laser has a power output of $1mW$ of light of wavelength $632.8nm$. Calculate the energy of each photon in eV (electron volt).

Answer 1

Hint:We know that energy of each photon is $E = hv$, where $h$ is Planck's constant and $v$ is frequency of photon. Speed of photon is product of frequency and wavelength of photon. Hence frequency is ration of speed of photon to wavelength of photon.

Complete step-by-step solution:We know that energy of each photon is $E = hv$, where $h$ is Planck's constant and $v$ is frequency of photon.
Given, the wavelength of a photon is $\lambda = 632.8nm = 632.8 \times {10^{ - 9}}m$.
A photon travels with the speed of light then its speed is $c$.
Speed of the photon is the product of the frequency and wavelength of the photon. Then
$c = \lambda \times v$ or $v = \dfrac{c}{\lambda }$
Put the value of frequency in energy equation we get,
$E = \dfrac{{h \times c}}{\lambda }$, where planck's constant h=$h = 6.626 \times {10^{ - 32}}J/s$ and $c = 3 \times {10^8}m/s$
$E = \dfrac{{\left( {6.626 \times {{10}^{ - 32}}} \right) \times \left( {3 \times {{10}^8}} \right)}}{{632.8 \times {{10}^{ - 9}}}}$
$E = 3.14 \times {10^{ - 19}}J$
We know that $1ev = 1.6 \times {10^{ - 19}}J$
Then, energy in eV (electron volt) is
$E = \dfrac{{3.14 \times {{10}^{ - 19}}}}{{1.6 \times {{10}^{ - 19}}}} = 1.96eV$
Hence the correct answer is option B.

Note:- Here the wavelength of each photon is the same and all photons have the same energy. Then we can find the number of photons emitted per second by dividing given power output with energy of one photon.