Energy and momentum of a photon is given by the expressions, energy \( E = h\nu \), and momentum \( p = \displaystyle\frac{h}{\lambda} \), respectively, where \( \nu \) is the frequency of photon, \( h \) is Planck's constant and \( \lambda \) is the wavelength of the photon. On the basis of the above statement, choose the option which is equal to the velocity of light?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( Ep^{-1} \)
For any wave, speed = frequency \( \times \) wavelength, so for light \( c = \nu\lambda \). Dividing the photon energy by its momentum brings out this product:
\( \displaystyle \frac{E}{p} = \frac{h\nu}{h/\lambda} = \nu\lambda = c \)
So \( c = E/p = Ep^{-1} \).
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Particle Nature of Light: The Photon – “… We can summarise the photon picture of electromagnetic radiation as follows: … (ii) Each photon has energy E (= hν) and momentum p (= hν/c), and speed c, the speed of light.”