Calculate the frequency of each of the following wavelengths of electromagnetic radiation.

• $632.8\, nm$ (wavelength of red light from a helium-neon laser). Express your answer using three significant figures.
• $503\, nm$ (wavelength of maximum solar radiation). Express your answer using three significant figures.
• $0.0520\, nm$ (a wavelength contained in medical X-rays). Express your answer using three significant figures.

In this question,  wavelengths of different types of electromagnetic waves are given to find the frequency.

Electromagnetic radiation is a form of energy that can be seen in daily life in the form of radio waves, X-rays, microwaves, and gamma-rays. Another type of this energy is sunlight, but daylight contributes to a small part of the spectral region of electromagnetic radiation including a wide variety of wavelengths.

The synchronized oscillations or periodic changes of magnetic and electric fields result in electromagnetic waves which make electromagnetic radiation. Contrasting electromagnetic spectrum wavelengths are generated which depends upon the occurrence of the periodic change and the power produced.

In this type of wave, the magnetic and electric fields which vary with time are unanimously associated at right angles and are perpendicular to the direction of motion. Electron radiations are emitted like photons once electromagnetic radiation takes place. These are light energy packages or gauged harmonic waves that progress at the speed of light. The energy is then classified according to its wavelength in the electromagnetic spectrum.

Let $v$ be the velocity, $\lambda$ be the wavelength, and $f$ be the frequency of the given electromagnetic radiations.

For red light from a helium-neon laser:

$\lambda=632.8\, nm=632.8\times 10^{-9}\,m$ and $c=3\times 10^8\,m/s$

Now since, $c=f \lambda$

Or  $f=\dfrac{c}{\lambda}$

$f=\dfrac{3\times 10^8}{632.8\times 10^{-9}}$

$f=4.74\times 10^{14}\,Hz$

$\lambda=503\, nm=503\times 10^{-9}\,m$ and $c=3\times 10^8\,m/s$

Now since, $c=f \lambda$

Or  $f=\dfrac{c}{\lambda}$

$f=\dfrac{3\times 10^8}{503\times 10^{-9}}$

$f=5.96\times 10^{14}\,Hz$

For medical X-rays:

$\lambda=0.0520\, nm=0.0520\times 10^{-9}\,m$ and $c=3\times 10^8\,m/s$

Now since, $c=f \lambda$

Or  $f=\dfrac{c}{\lambda}$

$f=\dfrac{3\times 10^8}{0.0520\times 10^{-9}}$

$f=5.77\times 10^{18}\,Hz$

Example 1

The wavelength of light is $6.4 \times 10^{-6}\,m$. Find its frequency.

Solution

Since the frequency of the light is required, therefore, its velocity is:

$c=3\times 10^8\,m/s$

Also as $\lambda =6.4 \times 10^{-6}\,m$ and $c=f\lambda$, so that:

$f=\dfrac{c}{\lambda}$

$f=\dfrac{3\times 10^8}{6.4 \times 10^{-6}}$

$f=0.469\times 10^{14}\,Hz$

Example 2

The frequency of a light is $3.3 \times 10^{-2}\,Hz$. Find its wavelength.

Solution

Since the wavelength of the light is required, therefore, its velocity is:

$c=3\times 10^8\,m/s$

Also as $f =3.3 \times 10^{-2}\,Hz$ and $c=f\lambda$, so that:

$\lambda=\dfrac{c}{f}$

$\lambda=\dfrac{3\times 10^8}{3.3 \times 10^{-2}}$

$f=0.91\times 10^{10}\,m$