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# Mass of a photon of frequency $v$ is given by:\begin{align} & A.\dfrac{hv}{c} \\ & B.\dfrac{h}{\lambda } \\ & C.\dfrac{hv}{{{c}^{2}}} \\ & D.\dfrac{h{{v}^{2}}}{c} \\ \end{align}

Last updated date: 17th Jun 2024
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Hint: Consider a light ray of frequency $\nu$, then the energy of the wave is given from the photoelectric effect. Similarly, the energy due to the particles of mass $m$ which are present in the light rays is given from the mass energy equivalence, using the two we can solve the question.
Formula: $E=hv$ and $E=hv$

We know that the light rays have dual nature and can be represented as waves of some frequency and as particles of some mass.
Then from the photo-electric effect the energy of the waves is given as $E=hv$, where $E$ is the energy of the photon which is produced due to light rays of frequency $v$ and $h$ is the Planck’s constant.
Similarly, the energy of the particle nature is given from mass energy relation, that the energy of any particle like photon in rest is the product of the mass $m$ of the particle with the speed of the light $c$ $E=mc^{2}$
Comparing the two equations, we get, $hv=mc^{2}$
$\therefore m=\dfrac{hv}{c^{2}}$

Hence the correct answer is option $D.\dfrac{h{{v}^{2}}}{c}$.