A neutron moving with a speed , v makes a head on collosion with a hydrogen atom in atom in ground state which is at rest. Choose the correct options (s) of the following (assume mass of neutron is nearly equal to the mass of hydrogen atom) .

Options

A. For the collision to the inelastic, the minimum value of kinetic energy of neutron before collision is `10.2eV`
B. For the collision to the elastic , the minimum value of initila kinetic energy of the neutron before collision is `10.2eV`
C. for any value of initial kinetic energy of neutron the collision may be elastic .
D. If initial Kinetic energy of neutron before collision is `27.2eV`, the collision may be elastic or inelastic or prefectly inelastic

Answer

A, C, D

Explanation

Let m , M be the masses of neutrons and hydrogen atom respectively . Maximum possible loss takes place in perfectly inelastic collision . From conservation of linear momentum mv+0=(M+m)v' where v' = common velocity after collision . Therefore Maximum possible loss in `Ke` is `DeltaK is DeltaK=1/2 mv^(2)-1/2(M+m)v^(2)`
i.e `DeltaK=1/2mv^(2)(m/M+m)1/2"mu"^(2)(m/(M+m))geDeltaE Rightarrow 1/2"mu"^(2)geDeltaE(1+m/M)`
i.e `KE_(min)=DeltaE(1+m/m)=10.2xx(1+1)=20.4eV`
If initial Ke of the neutron is less than `20.4eV`, loss in `KE` will less than 20.2eV hence electron can't be excited hence atom can't absorb any energy internally and hence there will no loss of Kinetic energy of the system . therefore the collision is elastic . Even through the potential loss in KE of the system is greater than or equal the excition energy, excitation may not take place necessarily hence there may not be loss in KE of the system hence for any value of initial KE of the neutrons the collision excitation should take place hence initial `KE` of the neutron should not be less than `20.4eV`. If initial `KE` of neutrons is `27.2eV`, maximum possible loss in `KE` is
` DeltaK=1/2"mu"^(2)(M/M+m)=27.2xx1/2=13.6eV`
this is enough to excite the electron and if this take place as both move together the collision is perfectly inelastic. The loss may be less than `13.6eV` (say`10.2eV`) , in this case excition may take place and as both can't move be inelastic .Excitation may not take place hence there may not be any loss iin `KE` actually , hence the collision may be elastic.