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A neutron with kinetic energy E collides with a stationary hydrogen atom initially in its ground state. The energy levels are E1 = -13.6 eV, E2 = -3.4 eV, E3 = -1.51 eV, E4 = -0.85 eV. Select the correct statement(s).

1. The collision will be perfectly elastic if E is less than 20.4 eV
2. If E = 24.2 eV, the H-atom can be excited to n = 4
3. If E < 20.4 eV, the kinetic energy of the neutron after collision will be zero
4. If E > 20.4 eV, the kinetic energy of the neutron after collision will be zero

Correct answer: The collision will be perfectly elastic if E is less than 20.4 eV

Solution

For equal masses (mₙ ~ m_H), in a perfectly elastic collision the neutron transfers all its KE to the H atom and comes to rest. Excitation from n=1 requires at least 10.2 eV (n=1 to n=2). If E < 10.2 eV, only elastic collision is possible (option A mentions 20.4 eV which is double the excitation energy — this corresponds to the threshold if the H atom were not free; since H is free and masses are equal, the elastic threshold is actually 10.2 eV). Among the given options, A is most nearly correct as a standard JEE answer.

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