Two hydrogen atom in ground state are moving on opposite direction with the same speed and collide head on . The minimum kinetic energy of each hydrogen atom for the collision to be inelastic so that both the atoms are excited is

Options

A. `13.6eV`
B. `10.2eV`
C. `20.4eV`
D. `27.2eV`

Answer

B

Explanation

Let K by the initial energy of each atoms . Maximum loss in Ke takes place in perfectly inelastic collision. From conservation of linear momentum `"mu"+(-"mu")=2mvRightarrowv=0`
Where v=common velocity after collision.
therefore maximum possible loss in KE is
` DeltaK=1/2"mu"^(2)xx2-1/22mxx0^(0)=21/2"mu"^(2)=2K` Minimum energy required to excite both the electrons is `DeltaE=10.2+10.2=20.4eV`. For inelastic collision with two electron excited
`DeltageDeltaERightarrow2Kge20.4RightarrowK_(min)=10.2eV`