A photon has a momentum of \( 3.3\times10^{-29}\,\mathrm{kg\,m/s} \). The frequency of the waves associated with the photon will be (Given: \( h = 6.6\times10^{-34}\,\mathrm{J\,s} \))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 1.5\times10^{13}\,\mathrm{Hz} \)
The momentum of a photon is \( p = h/\lambda \), and its wavelength and frequency are related by \( \lambda = c/\nu \). Combining the two gives the frequency in terms of the momentum.
\( \displaystyle p = \frac{h}{\lambda} = \frac{h\nu}{c} \;\Rightarrow\; \nu = \frac{p\,c}{h} \)
Taking \( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \):
\( \displaystyle \nu = \frac{3.3\times10^{-29} \times 3\times10^{8}}{6.6\times10^{-34}} = \frac{9.9\times10^{-21}}{6.6\times10^{-34}} = 1.5\times10^{13}\,\mathrm{Hz} \)
Note: A similar question was also asked in CUET (UG) 2023 on 13-06-2023 (Slot 1).