Question

The effective mass of photon in microwave region, visible region and X-ray region is in the following order:
(A) Microwave > X-ray > Visible
(B) X-ray > Microwave > Visible
(C) Microwave > Visible> X-ray
(D) X-ray > Visible > Microwave

Answer 1

Hint
- We will first rank the waves in an increasing order of wavelength.
- Then, we will use de-Broglie’s wavelength to establish a relation between effective mass and wavelength of a photon.
- Finally, we will reverse the order of wavelength to get the order of its effective mass as wavelength is inversely proportional to the mass of the photon.

Complete step by step answer
According to the electromagnetic spectrum, there are different regions of waves categorised based on their applications and characteristics. Each of them has unique properties of wavelength. Following is a table for the wavelength of waves lying in X-ray, Visible and Microwave regions.

Electromagnetic Region	Wavelength (in angstroms)
X-ray	0.1 A -100 A
Visible	4000 A - 7000 A
Microwave	${10^7}$ A – ${10^{10}}$ A

From the table we know the order of increasing wavelength. It is written below: -
X-ray < Visible < Microwave
Now, we know that every wave has a particle nature. So, we will use the wave particle duality to determine the order of effective mass of the photon. According to De-Broglie wavelength of a photon is given by the following formula: -
$\Rightarrow \lambda = \dfrac{h}{p}$
Where,
$\Rightarrow \lambda$ = wavelength.
h = Planck’s constant $\left( { = 6.636 \times {{10}^{ - 34}}} \right)$
p = momentum.
We know that momentum = mass x velocity. Thus, substituting $p = mv$ in the above equation we get:
$\Rightarrow \lambda = \dfrac{h}{{mv}}$
Now, in this equation we observe that $\lambda$ is inversely proportional to the mass. This means that the mass of the photon will decrease as the wavelength increases. Thus, the order of effective mass of the photon becomes: -
$\Rightarrow$ X-ray > Visible > Microwave
Hence, option (D) is the correct solution.

Note
Since, it is a very tedious task to remember the wavelengths for all the regions in the electromagnetic spectrums it is suggested to learn the order of regions for increasing wavelengths to be able to attempt such questions. The order of electromagnetic regions for increasing wavelengths is given below: -
X-rays < Ultraviolet Rays < Visible Light < Infra-Red Rays < Microwaves < Radio waves