Question

To which part of the electromagnetic spectrum does a wave of frequency $5\times {{10}^{11}}Hz$ belong?

Answer 1

Hint: We need to know the classification of waves according to their frequencies to solve this question. Here, we will discuss this classification of the EM spectrum based on frequency. Then we will find out where the given frequency lies in the spectrum.

Complete answer:
We must know that electromagnetic radiations are classified into different categories of waves according to the frequency of the wave. The types of waves that are categorized into includes, radio waves, microwaves, infrared region, visible light, ultraviolet radiation, X-rays, and gamma rays.

The following table lists frequency ranges of the divisions of the electromagnetic spectrum.

Category	Range of frequency (Hz)
Gamma rays	Greater than $3\times {{10}^{17}}Hz$
X-rays	\[3\times {{10}^{16}}Hz\text{ to }3\times {{10}^{17}}Hz\]
Ultraviolet light	\[7.5\times {{10}^{14}}Hz\text{ to }3\times {{10}^{16}}Hz\]
Visible light	\[4.3\times {{10}^{14}}Hz\text{ to }7.5\times {{10}^{14}}Hz\]
Infrared	\[3\times {{10}^{12}}Hz\text{ to }4.3\times {{10}^{14}}Hz\]
microwave	\[3\times {{10}^{9}}Hz\text{ to }3\times {{10}^{12}}Hz\]
Radio waves	Less than \[3\times {{10}^{9}}Hz\]

In this given spectrum, only the visible light could be observed by human eyes. Gamma rays are used to kill bacteria and sterilize medical equipment. X-rays are usually used for image bone structures. Infrared is used in heat sensors, laser metal cutting etc. microwaves are used in ovens and radio waves are used for communication and broadcasting.

Now, the given frequency in the question is $5\times {{10}^{11}}Hz$ . It is situated in a microwave which ranges from \[3\times {{10}^{9}}Hz\text{ to }3\times {{10}^{12}}Hz\] . Therefore, wave with frequency $5\times {{10}^{11}}Hz$ is in the microwave region of the electromagnetic spectrum.

Note:
We can also classify the electromagnetic spectrum on the basis of wave length. We can use the relation between frequency and wavelength which is given as $\upsilon =\dfrac{c}{\lambda }$ to convert the given frequency ranges into wavelengths. $c$ in the expression is velocity of light. So, if we are classifying EM spectrum on the basis of wavelength, radio waves will be having the largest wavelength and gamma rays will be having the smallest.