A hydrogen atom moving at a speed $v$ absorbs a photon of wavelength 122 nm and stops. Find the value of $v$. Mass of a hydrogen atom $1.67\times {10}^{-27}kg$.

The linear momentum of the photon is

$p=\frac{h}{\lambda }=\frac{6.63\times {10}^{-34}}{122\times {10}^{-9}}=5.43\times {10}^{-27} {\mathrm{kgms}}^{-1}$

As the photon is absorbed and the atom stops, the total final momentum is zero.

From conservation of linear momentum, the initial momentum must be zero. The atom should move opposite to the direction of motion of the photon and they should have the same magnitudes of linear momentum.

$$\begin{gathered} \Rightarrow \left(1.67\times {10}^{-27} \mathrm{kg}\right)v=5.43\times {10}^{-27} {\mathrm{kgms}}^{-1} \\ \Rightarrow v=\frac{5.43\times {10}^{-27}}{1.67\times {10}^{-27}} {\mathrm{ms}}^{-1}=3.25 {\mathrm{ms}}^{-1} \end{gathered}$$