Physics - Rotation Question with Solution | TestHub

Let mass of hydrogen atom be m and initial velocity of helium be u . therefore from momentum conservation (for maximum loss of energy) $4mu=4m{v}_1+m{v}_1\Rightarrow v_1=\frac{4v}{5}$ Loss in kinetic energy $=\frac{1}{2}4m{u}^2-\frac{1}{2}5m{\left(\frac{4u}{5}\right)}^2=\left(\frac{1}{2}4m{u}^2\right)\left(1-\frac{4}{5}\right)=\frac{1}{5}\left(K{E}_i\right)$ Loss in KE must be equal to the sum of excitation energy for helium and hydrogen atom $\therefore 10.2\mathrm{eV}+40.8\mathrm{eV}=\frac{1}{5}K{E}_i=(51)\times 5\mathrm{eV}=255\mathrm{eV}$