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

Explanation

Let `K` be the kinetic energy of the moving hydrogen atom `K`' the kinetic energy of combined mass after collision.
From conservation of liner momentum .
`p = p' implies sqrt (2 K m) = sqrt(2 K' (2 m))`
or `K = 2K'`
From conservation of energy
`K = K' + Delta E`
Solving Eqs. (i) and (ii), we get `Delta E = (K)/(2)`
Now, minimum value of `Delta E` for hydrogen atom is `10.2 e V`.
or `Delta E ge 10.2 e V`
`:. (K)/(2) ge 10.2 e V`
`:. K ge 20.4 e V`

Therefore, the minimum kinetic energy of moving hydrogen is `20.4 e V`