In equation \( P = Ec^{-1} \), where P is momentum, E is energy and c is the speed of light. In which of the following options, this equation is valid:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → for a photon but not for an electron
The energy and momentum of any particle are linked by the relativistic energy-momentum relation, where \( m_0 \) is the rest mass:
\( \displaystyle E^{2} = p^{2}c^{2} + m_0^{2}c^{4} \)
A photon has zero rest mass, so \( E = pc \), that is \( p = E/c \). An electron has a rest mass, so \( E \) is always greater than \( pc \) and \( p = E/c \) does not hold for it. (At low speed its kinetic energy is \( p^{2}/2m \), which is again not \( pc \).)
Option (1) for an electron only — Incorrect. The relation needs zero rest mass, and the electron has a rest mass.
Option (2) for a photon but not for an electron — Correct. It holds for the massless photon and fails for the electron.
Option (3) for an electron as well as for a photon — Incorrect. It does not hold for the electron, because of its rest-mass term.
Option (4) neither for an electron nor for a photon — Incorrect. It does hold for a photon, whose energy is \( h\nu \) and momentum \( h/\lambda = h\nu/c \).
NCERT (2026-27):
Particle Nature of Light: The Photon – “… (ii) Each photon has energy E (= hν) and momentum p (= hν/c), and speed c, the speed of light.”