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Question: The mass of photon having wavelength 1nm is: a.) \(2.21 \times {10}^{-35} kg\) b.) \(2.21 \time...

The mass of photon having wavelength 1nm is:
a.) 2.21×10−35kg2.21 \times {10}^{-35} kg
b.) 2.21×10−33g2.21 \times {10}^{-33} g
c.) 2.21×10−33kg2.21 \times {10}^{-33} kg
d.) 2.21×10−26kg2.21 \times {10}^{-26} kg

Explanation

Solution

Photon is a quantum of electromagnetic radiation. They are always in motion. The energy of a photon depends upon the radiation frequency. The wavelength is given as:
λ=hmv\lambda \quad =\quad \cfrac { h }{ mv }

Complete Solution :
- A photon is a very tiny particle which comprises electromagnetic radiation. These are just electric fields travelling through space. They don't have any charge, or resting mass and tend to travel at the speed of light. Since they are very small in size, they contribute to the wavelike characteristic. Every wave or a wavelike path has a wavelength. It is the distance between two successive wave crests or troughs. Light has dual nature which means it has both particle nature as well as wave nature. Therefore, the wavelength of the photon is inversely proportional to the momentum of the photon and thus can be written as:
λ=hmv\lambda \quad =\quad \cfrac { h }{ mv }
where λ=wavelength\lambda = wavelength, h=planck's constant, m=mass of the photon and v=velocity of photon.
- We know that the photon travels with the speed of light, c. Therefore, v=c. Replacing v by c, we get
λ=hmc\lambda \quad =\quad \cfrac { h }{ mc }
Now, we need to find the mass of the photon with wavelength = 1×10−9m1 \times {10}^{-9} m. Therefore, the above formula can be re-written as follows.
m=hλcm\quad =\quad \cfrac { h }{ \lambda c } ----(1)
- The values of h and c are 6.26×10−346.26 \times {10}^{-34} and 3×108m/s3 \times {10}^{8}m/s respectively. Substituting these values in equation (1), we get,
m=6.26×10−341×10−9×3×108m\quad =\quad \cfrac { 6.26\quad \times \quad { 10 }^{ -34 } }{ 1\quad \times \quad { 10 }^{ -9 }\quad \times \quad 3\quad \times \quad { 10 }^{ 8 } }
  ⟹  m=2.21×10−33kg\implies m\quad =\quad 2.21\quad \times \quad { 10 }^{ -33 }\quad kg
Therefore, the mass of the photon with wavelength 1×10−9m1 \times {10}^{-9} m is 2.21×10−33kg2.21 \times {10}^{-33} kg.
So, the correct answer is “Option C”.

Note: Photon has a negligible mass, but in this question we are said to consider it in particle nature as we are asked to find out the mass of a photon. And the mass of the photon does depend upon the wavelength of the photon.