(a) Calculate the energy and momentum of a photon in a monochromatic beam of wavelength 331.5 nm. (b) How fast should a hydrogen atom travel in order…

$\displaystyle \operatorname{momentum}(p)$ $$\begin{aligned} & \quad p=\frac{h}{\lambda} \\ & =\frac{6 \cdot 63 \times 10^{-34}}{331 \cdot 5 \times 10^{-9}} \\ & p=2 \times 10^{-27} \mathrm{~kg} \mathrm{~ms}^{-1} \\ & \text { (b) Momentum of H atom }=\text { momentum of the photon }=2 \times 10^{-27} \mathrm{~kg} \mathrm{~ms}^{-1} \\ & p=m u \\ & u=\frac{p}{m}=\frac{2 \times 10^{-27}}{1 \cdot 67 \times 10^{-27}} \mathrm{~ms}^{-1} \\ & u=1 \cdot 20 \mathrm{~ms}^{-1} \end{aligned} $$