A moving hydrogen atom makes a head on collision with a stationary hydrogen atom. Before collision both atoms are in in ground state and after collision they move together. What is the minimum value of the kinetic energy of the moving hydrogen atom, such that one of the atoms reaches one of the excited state?

Explanation

Let `K` be the kinetic energy of the moving hydrogen atom and `K`, the kinetic energy of combined mass after collision.
From conservation of linear momentum,
`p=p'or sqrt(2KM)=sqrt(2K'(2m))` ltbr. or `K=2K'`.....(i)
From conservation of enrgy, `K=K^(+)+DeltaE`....(ii)
Solving Eqs. (i) and (ii), we get `DeltaE=(K)/(2)`
Now minimum value of `DeltaE` for hydrogen atom is `10.2 eV`.
or `Delta gt10.2eV`
`:. (K)/(2) ge10.2`
`:. K ge20.4 eV`
Therefore, the minimum kinetic energy of moving hydrogen is `20.4 eV`