Question

Calculate the wavelength, in meters, of radiation with a frequency of $1.18 \times {10^{14}}{s^{ - 1}}.$ What region of the electromagnetic spectrum is this?

Answer 1

Hint: The relationship between the wavelength and frequency of a radiation is depicted by a simple equation which includes the wavelength term, the frequency term and a constant term which connects them. On substituting the value for wavelength term in the equation, we can obtain the value of frequency, and vice versa.

Complete answer:
Wavelength is the distance between two adjacent crests or troughs of a wave. The wave can be an electromagnetic wave, sound wave et cetera. The SI unit of wavelength is metre (m).
Frequency is the number of waves that pass through a given point in unit time. The SI unit of frequency is Hertz (Hz). It is also measured in ${s^{ - 1}}.$
The equation that relates frequency with wavelength is as follows:
$c = \nu \,\lambda $
Where,
$\lambda $ is the wavelength of the wave,
$\nu $ is the frequency of the wave,
$c$ is the speed of light in vacuum. It has a constant value, $c = 3 \times {10^8}\;m{s^{ - 1}}.$
In the question, we are given that the frequency of the radiation is $1.18 \times {10^{14}}{s^{ - 1}}.$ The wavelength of the radiation is calculated as:
$\lambda = \dfrac{c}{\nu }$
$\lambda = \dfrac{{3 \times {{10}^8}\;m{s^{ - 1}}\,}}{{1.18 \times {{10}^{14}}{s^{ - 1}}}}$
$ = 2.54 \times {10^{ - 6}}m$
This lies in the Infrared (IR) region $\left( {{{10}^{ - 6}}m\,\,{\text{or}}\,\,\mu m} \right)$ of the electromagnetic spectrum.

Note:
The electromagnetic spectrum is the range of increasing wavelengths or decreasing frequencies of electromagnetic waves arranged in order. The order of the series is as follows: Gamma rays, X-rays, UV- rays, Visible spectrum, Infrared, Microwaves and Radio waves. Electromagnetic radiation can be expressed in terms of energy, wavelength, or frequency.