Question

Two hydrogen atoms moving at the same speed in opposite directions collide up with zero kinetic energy. Each atom then emits light with a wavelength of 121.6 nm. At what speed were the atoms moving before the collision considering that the mass of a hydrogen atom is equal to that of a proton?

Answer 1

The kinetic energy, $K=\frac{1}{2}mu^{2}$ of hydrogen was released in form of photon.

Energy of a photon, $E=\frac{hc}{\lambda}$

Therefore $\frac{1}{2}mu^{2} =\frac{hc}{\lambda}$

$\frac{1}{2} \times1.67\times10^{-27}\times$ $u^{2} = \frac{6.626\times10^{-34}\times3\times10^{8}}{121.6\times10^{-9}}$

$u=4.43\times10^{4}ms^{-1}$