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**Hint:**The question gives us the value of wavelength, speed and Planck’s constant. We will calculate the mass of the photon using de Broglie’s equation:

$\lambda = \dfrac{h}{{mc}}$

**Complete step by step solution:**

-First of all, let us talk about the de-Broglie equation for a photon.

The de-Broglie equation describes the wave nature of an electron. An electromagnetic equation exhibits dual nature: of a particle because it has momentum and wave because it has both wavelength and frequency. The de-Broglie equation exhibits the relationship between the momentum of a particle and its wavelength and so the wavelength is known as de-Broglie wavelength. Mathematically this equation for a photon is:

$\lambda = \dfrac{h}{{mc}}$-------- (1)

Where, λ = de-Broglie wavelength;

$h$ = Planck’s constant = $6.6252 \times {10^{ - 34}}kg.{m^2}/s$;

$c$ = velocity of light = $3 \times {10^8}$ metre/second;

$m$ = mass of particle.

-The question gives us the value of wavelength is 5894$\mathop {\rm A}\limits^ \circ $ and we need to calculate the mass of the photon. We will do this using the de-Broglie equation (1):

$λ$ = 5894$\mathop {\rm A}\limits^ \circ $ = $5894 \times {10^{ - 10}}$ m

$h$ = $6.6252 \times {10^{ - 34}}kg.{m^2}/s$

$c$ = $3 \times {10^8}$ metre/second

$\lambda = \dfrac{h}{{mc}}$

$5894 \times {10^{ - 10}} = \dfrac{{6.6252 \times {{10}^{ - 34}}}}{{m \times 3 \times {{10}^8}}}$

$m = \dfrac{{6.6252 \times {{10}^{ - 34}}}}{{3 \times {{10}^8} \times 5894 \times {{10}^{ - 10}}}}$

= $\dfrac{{6.6252 \times {{10}^{ - 34}}}}{{17682 \times {{10}^{ - 2}}}}$

= $3.746 \times {10^{ - 36}}$ kg

Hence we can now tell that the mass of the photon of sodium will be $3.746 \times {10^{ - 36}}$ kg.

**So, the correct option will be: $3.746 \times {10^{ - 36}}$ kg.**

**Note:**The mass ‘m’ we calculate here is the relativistic mass and not the rest mass because the rest mass of a photon is always zero (0).

Also if a particle moves with velocity v, the momentum of the particle will be: p = mv and the de-Broglie wavelength will be:

$\lambda = \dfrac{h}{{mv}}$

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