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

An `H` atom in ground state is moving with initial kinetic energy `K`

1.	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.A. `63.75eV`B. `51eV`C. `54.4eV`D. `13.05eV`
Answer» Correct Answer - A 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`

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

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