Question

A helium-neon laser emits red light having a wavelength of $632.8\;nm$. Calculate the frequency of light emitted by the $He - Ne$ laser. Use speed of light $c = 2.998 \times {10^8}m{s^{ - 1}}$?

Answer 1

The wavelength, frequency and speed of light are correlated. Helium-neon lasers give the electromagnetic radiation of red colour, i.e. of visible range. The frequency of a radiation can be expressed by $\nu$ (nu) and the unit is per second ${s^{ - 1}}$ or $Hertz(Hz)$ .

Complete answer:
The relation between frequency, wavelength and speed of light is given as - $c = \nu \lambda$ , where,
c = speed of light = $c = 2.998 \times {10^8}m{s^{ - 1}}$
$\lambda$ = wavelength = $632.8\;nm$ and
$\nu$ = frequency = ?
First, we need to convert the wavelength into meters from nanometers. This can be done as –
$632.8\;nm \cdot \dfrac{{1m}}{{{{10}^9}nm}} = 6.328 \times {10^{ - 7}}m$
Now, using this relation, the frequency can be calculated as –
Frequency = speed of light / wavelength or $\nu = \dfrac{c}{\lambda }$
Now, putting values, we have –
\eqalign{ & \nu = \dfrac{{2.998 \times {{10}^8}m{s^{ - 1}}}}{{6.328 \times {{10}^{ - 7}}m}} \cr & \nu = 4.738 \times {10^{14}}Hz \cr}
Hence, the frequency of red light emitted by the $He - Ne$ laser will be $\nu = 4.738 \times {10^{14}}Hz$

Note:
If we know the value of any two of the three variables i.e. wavelength, frequency and speed of light, then the value of the third variable can be calculated by the given formula. The units should be noted carefully and proper conversion should be made accordingly. The unit of wavelength should be in meters, the speed of light in meters per second and frequency in per second or hertz.