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

Given:

$\lambda =656.3M_H=1.67\times {10}^{-27}$

a)
$\lambda =656.3nm$
Mometum $P=E/C=\frac{hc}{C\lambda }=\frac{h}{\lambda }=\frac{6.63\times {10}^{-34}}{656.3\times {10}^{-9}}=0.01\times {10}^{-25}=1\times {10}^{-27}kg-m/s$

b)

$P=mV$
$1\times {10}^{-27}=1.67\times {10}^{-27}\times v$
$\Rightarrow V=1/1.67=0.598=0.6m/s$

c)
KE of atom = $1/2\times 1.67\times {10}^{-27}\times (0.6{)}^2=\frac{0.3006\times {10}^{-27}}{1.6\times {10}^{-19}}ev=1.9\times {10}^{-9}eV$.