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# 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?

Last updated date: 05th Aug 2024
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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.

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.