Suppose a moving hydrogen atom makes a head on inelastic collision with a stationary hydrogen atom. Before collision, both atoms are ground state and after collision, they move together. What is the minimum velocity of the moving hydrogen atom if one of the atoms is to be given the minimum excitation energy after the collisions? Take `m_H=1.0078 am u. 1.66xx10^(-27)kg.`

Explanation

Let u be the minimum velocity of moving hydrogen atom before collision and v be the velocity with which both move together after collision. form the law of conservation of linear momentum.
`mxxu+mxx0=(m+m)v`
`v=u//2`
Let `DeltaK` be the loss in kinetic energy on collision.
`DeltaK=1/2m u^2-1/2(m+m)v^2`
`=1/2m u^2-1/2xx2m(u//2)^2=1/4m u^2`
Minimum excitation energy `=E_2-E_1`
`=(-13.6)/(2^2)-((-13.6)/(1^2))=10.2eV`
`=10.2xx1.6xx10^(-19)J=16.32xx10^(-19)J`
`:. 1/4m u^2=16.32xx10^(-19)`
`u=sqrt((4xx16.32xx10^(-19))/(1.0078xx1.66xx10^(-27)))`
`u=6.24xx10^4 m//s`