Question

When a photon is emitted by a hydrogen atom, the photon carries a momentum with it.

(a) Calculate the momentum carried by the photon when a hydrogen atom emits light of wavelength 656.3 nm.

(b) With what speed does the atom recoil during this transition ? Take the mass of the hydrogen atom = $1.67\times {10}^{-27}$ kg.

(c) Find the kinetic energy of recoil of the atom.

Answer 1

(a) Here $\lambda$ = 656.3 nm

momentum 'P' = $\frac{E}{c}=\frac{hc}{\lambda }\times \frac{1}{c}=\frac{h}{\lambda }$

= $\frac{6.63\times {10}^{-34}}{656.3\times {10}^{-9}}$

= $0.01\times {10}^{-25}$

= $1\times {10}^{-27}kg-m/s$

(b) $1\times {10}^{-27}=1.67\times {10}^{-27}\times v$

$\Rightarrow v=\frac{1}{1.67}$

= 0.598 = 0.6 m/s

(c) KE of atom = $\frac{1}{2}\times 1.67\times {10}^{-27}\times (0.6{)}^2$

= $\frac{0.3006\times {10}^{-27}}{1.6\times {10}^{-19}}eV$

= $1.9\times {10}^{-9}eV$