Question

Which of the following has maximum energy?
A) Radio waves
B) X-rays
C) Light waves
D) Microwaves

Answer 1

Hint: To find which of the given radiation have maximum energy, we have to find the quantities on which the energy of the radiation depends. This means to try to find the physical quantities which will affect the energy values. Now, find the characteristic features of the type of radiations given in the question and use that to explain their energy values.

Complete answer:
First, we will find the physical attributes such as frequency and wavelength of each option given in the question. But here the waves do not have a single value of frequency and wavelength but have a spectrum of frequency and wavelength which can be used to explain the characteristics of each wave.
The radio waves have a frequency ranging from $300GHz$ to $3kHz$ and their wavelength is between $1mm$ to $100km$. Similarly, light waves have a frequency from $400THz$ to $790THz$ and wavelengths of $380nm$ to $750nm$. X-rays have a frequency from $30petaHz$ to $30hexaHz$ and wavelengths of $10pm$ to $10nm$. And lastly, microwaves have a frequency from $300GHz$ to $300MHz$ and wavelengths of $1mm$ to $1m$.
Now, according to Max Planck, the energy of the radiation is given by,
$E = h\nu $
$ \Rightarrow E = \dfrac{{hc}}{\lambda }$
Where,
$E$ is the energy of radiation.
$h$ is Planck’s constant.
$\nu $ is the frequency of the radiation.
$\lambda $ is the wavelength of the wave.
$c$ is the speed of light.
As Planck’s constant and speed of light is constant, we can say that the energy is inversely proportional to the wavelength of the radiation and directly proportional to the frequency of the radiation. This implies that if there is an increase in the frequency or a decrease in the wavelength, the energy will increase in this case.
On comparing the wavelengths and frequencies of all the radiations, we can conclude that X-rays have the maximum frequency and minimum wavelength among all the given options. Hence, X-rays have maximum energy.
Therefore, option (B) is correct.

Note:
Max Planck discovered that energy is quantized. This means that each energy level can accommodate a certain amount of energy. This energy comes in a packet of photons and is an integral multiple of $h\nu $. Therefore, energy is discrete and not continuous.
Light is also electromagnetic radiation but it has a dual nature. It has the properties of the particle as well as of the wave. The photoelectric effect and Compton Effect explain the particle nature of the light. Interference and diffraction phenomena are used to explain the wave nature of light.