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 kinetic energy of the moving hydrogen atom andn K' , the kinetic energy of combined mass of after collision. Form conservation of linear momnetum,
`p=p'or sqrt(2Km)=sqrt(2K'(2m))orK=2k'" " ....(i) `
From conservation of energy,
`K=K'DeltaE" " ....(ii)`

Solving Eqs. (i) and (ii) we get
`DeltaE(K)/(2)`
Using the relation, `DeltaE=-13.6 Z^(2)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
For `n_(1)=1 and n_(2)=2` we get,
`DeltaE=-13.1(1)^(2)((1)/((1)^(2))-(1)/(2^(2)))=10.2 eV" " ( :.Z=1)`
So, minimum value of `DeltaE` for hydrogen atom is 10.2 eV.
or `" " DeltaEge10.2 eV`
`:. " " (K)/(2)ge10.2`
`:." " Kge20.4 eV`
Therefore, the minimum kinetic energy of moving hydrogen is 250.4 eV