Question

All components of the electromagnetic spectrum in vacuum have the same:
A) Energy
B) Velocity
C) Wavelength
D) Frequency

Answer 1

Hint:There are a number of electromagnetic waves such as gamma waves, infrared waves, radio waves, etc. We all know that light travels at a constant speed of $3 \times {10^8}m{s^{ - 1}}$. In wave theory light is considered a type of Electromagnetic wave.

Complete step by step answer:
Electromagnetic waves as the name suggests are made by combining the electric and magnetic fields. The fields are transverse in nature, they are always in phase and in 90 degrees with each other. The vibrations caused in the electric and magnetic field is the reason behind the production of EM waves.

Step 1: Discuss about the energy of EM waves in vacuum.
The energy of the EM wave is given by:
$E = \dfrac{{hc}}{\lambda }$;
Where:
E = Energy;
h = Planck’s Constant;
c = Speed of light;
$\lambda $ = Wavelength;
Suppose we move from radio waves to the gamma waves. Now the wavelength of radio waves ranges from 30cm to thousands of meters and the wavelength of gamma waves ranges from ${10^{ - 12}}$meters to ${10^{ - 13}}$meters. There is a huge difference between the wavelengths of the two waves. According to the formula the energy of the rays is inversely proportional to the energy, so, option “1” is ruled out.

Step 2: Wavelength and Frequency of EM waves in vacuum.
As we have already discussed, the wavelength of the EM waves are not constant, so, Option ”3” is ruled out. The frequency of the EM wave is given as:
$f = \dfrac{c}{\lambda }$ ;

Where:
c = Speed of light;
$\lambda $ = Wavelength;
f = Frequency;
According to the given formula of frequency for EM waves the frequency of the EM wave is inversely proportional to the wavelength and hence if the wavelength changes so does the frequency. Option “4” is ruled out.

Step 3: Velocity of the EM waves. The electromagnetic waves propagate through the vacuum at the speed of $3 \times {10^8}m{s^{ - 1}}$ since there is no resistance and distortion of any kind the speed of EM waves is equivalent to the speed of light. If the EM wave propagates through a medium then the speed will be less than the speed of light. Option “2” is valid.

Final Answer:Option “2” is correct. All components of the electromagnetic spectrum in vacuum have the same velocity.

Note:Here, explore each of the given options and give a logical reason as to why that option is not constant in vacuum for the EM wave. Make proper relation between the wavelength, velocity, frequency and Energy and due to the variability of a few factors such as wavelength, frequency all the factors are also variable as they are related with each other.