A hydrogen atom moves with the same momentum as a photon of wavelength 600 nm. The speed of the hydrogen atom is (Take \(h = 6.6\times10^{-34}\ \mathrm{J\,s}\) and mass of the hydrogen atom \(= 1.67\times10^{-27}\ \mathrm{kg}\).)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(0.66\ \mathrm{m\,s^{-1}}\)
A photon of wavelength \( \lambda \) carries a momentum \( p=h/\lambda \). The hydrogen atom has the same momentum, so its speed is \( v=p/m \).
\( \lambda=600\ \mathrm{nm}=6.0\times10^{-7}\ \mathrm{m} \)
\( \begin{aligned} p &= \frac{h}{\lambda} \\ &= \frac{6.6\times10^{-34}}{6.0\times10^{-7}} \\ &= 1.1\times10^{-27}\ \mathrm{kg\,m\,s^{-1}} \end{aligned} \)
\( \begin{aligned} v &= \frac{p}{m} \\ &= \frac{1.1\times10^{-27}}{1.67\times10^{-27}} \\ &= 0.66\ \mathrm{m\,s^{-1}} \end{aligned} \)
From the above, \( v=0.66\ \mathrm{m\,s^{-1}} \). Hence, a slow-moving hydrogen atom already has as much momentum as a photon of visible light.
NCERT (2026-27):
Particle Nature of Light: the Photon – “(iii) All photons of light of a particular frequency ν, or wavelength λ, have the same energy E (=hν = hc/λ) and momentum p (= hν/c= h/λ), whatever the intensity of radiation may be. …”