Question

How can I calculate the wavelength of radio waves?

Answer 1

Radio waves are those waves which have the lowest frequency in the electromagnetic spectrum.
The wavelength, velocity and frequency are related by the equation:
$c=\upsilon .\lambda$

Complete answer:
In the question it is asked how we can calculate the wavelength of radio waves. Before going into the solution we have to know the terms frequency, wavelength, electromagnetic radiations and also about the radio waves.
We all are familiar with these terms from dealing with quantum mechanics in physical chemistry. We study about the wave and particle nature of the electron and describe its dual nature with the aid of these parameters. So very quickly let’s take a recap of these terms.
-Frequency – it is the measure of the number of waves that is passing through a fixed point in a certain time interval and they are measured in waves per second or cycles per second. And the unit is Hertz, it is generally defined as one wave per second.
-Wavelength-It is a parameter which is reciprocal to the frequency of the waves of the wave and wavelength is defined as the distance between two adjacent crests of a wave.
-Electromagnetic radiations-these are those radiations which transmits or radiate the energy through as the function of periodic oscillation of magnetic field and electric field is called the electromagnetic radiation and in electromagnetic radiations the electric field and magnetic fields are perpendicular to each other.
The electromagnetic radiations are divided into many in accordance to frequency and wavelength either in increasing order or decreasing order.
The radiation with the least frequency is the radio frequency and hence with largest wavelength.
We can find the wavelength of radio waves by solving the equation that relates frequency, wavelength and velocity for wavelength.
The equation is $c=\upsilon .\lambda$
Rearrange this equation for wavelength,
$\text{ }\\!\\!\lambda\\!\\!\text{ =}\dfrac{\text{c}}{\text{ }\\!\\!\upsilon\\!\\!\text{ }}$
So if we know the values of frequency and velocity we could find the value of wavelength of the radiation.
The typical frequency of radio waves ranges in between $\text{88-108MHz}$ and the wavelength of the radiation is about $\text{3}\text{.41 }\\!\\!\times\\!\\!\text{ 1}{{\text{0}}^{\text{9}}}\text{-2}\text{.78 }\\!\\!\times\\!\\!\text{ 1}{{\text{0}}^{\text{9}}}\text{nm}$

Note:
If the value of energy of the radiation and velocity of the radiation is given then we could find the value of wavelength using Planck’s equation.
The equation is as follows,
$\text{E=h }\\!\\!\upsilon\\!\\!\text{ =h}\dfrac{\text{c}}{\text{ }\\!\\!\lambda\\!\\!\text{ }}$
$\text{ }\\!\\!\lambda\\!\\!\text{ =h}\dfrac{\text{c}}{\text{E}}$