(a)

Calculate the energy and momentum of a photon in a monochromatic beam of wavelength $\displaystyle 331.5$ nm.

(b)

How fast should a hydrogen atom travel in order to have the same momentum as that of the photon in part (a) ?

$\displaystyle \operatorname{momentum}(p)$\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} $$