Which of the following physical quantities have the same value for electron and photons of same wavelength?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Momentum
The wavelength of a particle and its momentum are tied by the de Broglie relation \( \lambda = h/p \), and a photon obeys the same relation, \( p = h/\lambda \). Two particles of the same wavelength therefore have the same momentum.
\( \displaystyle p_{\mathrm{electron}} = \frac{h}{\lambda} = p_{\mathrm{photon}} \)
Why the other options are incorrect
Option (1) Energy — Incorrect. For the same momentum the photon has \( E = pc \), but the electron has \( E = \frac{p^{2}}{2m} = \frac{pv}{2} \), which is much smaller since \( v \ll c \).
Option (2) Angular momentum — Incorrect. The wavelength fixes only the momentum. It says nothing about the angular momentum, which depends on the orbit or on the intrinsic spin of the particle.
Option (4) Velocity — Incorrect. A photon always travels at c, while an electron of the same momentum moves at \( v = p/m \), far below c.
NCERT (2026-27):
Wave Nature of Matter – “… Equation (11.5) for a material particle is basically a hypothesis whose validity can be tested only by experiment. However, it is interesting to see that it is satisfied also by a photon. For a photon, as we have seen,
\( \displaystyle p = h\nu/c \qquad (11.6) \)
Therefore,
\( \displaystyle \lambda = \frac{h}{p} = \frac{c}{\nu} \qquad (11.7) \)
That is, the de Broglie wavelength of a photon given by Eq. (11.5) equals the wavelength of electromagnetic radiation of which the photon is a quantum of energy and momentum.”