What would be the effective mass of a photon, if the frequencies of radiation is \( 6 \times 10^{14}\,\mathrm{Hz} \) ?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 4.4 \times 10^{-36}\,\mathrm{kg} \)
A photon has no rest mass, but its energy \( E = h\nu \) corresponds to an effective mass through Einstein's mass-energy relation \( E = mc^{2} \).
\( \displaystyle m c^{2} = h\nu \;\Rightarrow\; m = \frac{h\nu}{c^{2}} \)
\( h = 6.63\times10^{-34}\,\mathrm{J\,s} \)
\( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \nu = 6\times10^{14}\,\mathrm{Hz} \)
\( \displaystyle m = \frac{6.63\times10^{-34} \times 6\times10^{14}}{(3\times10^{8})^{2}} = \frac{3.98\times10^{-19}}{9\times10^{16}} \approx 4.4\times10^{-36}\,\mathrm{kg} \)