An `H` atom in ground state is moving with initial kinetic energy `K` .It collides head on with `He ^(+)` ion in ground state kept at rest but free to move. Find minimum value of `K` so that both the particles can excite to their first excited state.

Options

A. `63.75eV`
B. `51eV`
C. `54.4eV`
D. `13.05eV`

Answer

A

Explanation

Max . Loss In `KE` of the system take place in perfectly inelastic collision . From conservation of linear momentum
` "mu"+0=(m+M)VRightarrow=("mu")/(m+M)
` Max. loss in `KE`
` DeltaK=1/2"mu"^(2)-1/2(M+m)V^(2)=1/2"mu"^(2)(M/(M+m))`
For both to get excited to their excited states, energy required is `DeltaE=10.2+10.2xx4=51eV`.
therefore For both to get excited
` DeltaKgeDeltaERightarrow1/2"mu"^(2)(M/(M+m))geDeltaE`
`Rightarrow 1/2"mu"geDeltaE(M+m)/m eVRightarrowKE_(min)=DeltaE(1+m/M)`
` i.e KE_(min)=51(1+1/4)=63.75eV`