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A neutron with kinetic energy E collides head-on with a stationary hydrogen atom in the ground state, where both the neutron and hydrogen atom have equal mass. The H-atom energy levels are: E1 = -13.6 eV, E2 = -3.4 eV, E3 = -1.51 eV. Elastic or inelastic nature of the collision depends on E. Choose 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 may get excited to n = 4.
3. If E < 20.4 eV the kinetic energy of the neutron will become zero after the collision.
4. If E > 20.4 eV the kinetic energy of the neutron will become zero after the collision.

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

Solution

The minimum CM energy needed to excite H from ground state to n=2 is 10.2 eV; with equal masses E_cm = E/2, so threshold is E = 20.4 eV. For E < 20.4 eV, collision is purely elastic — equal-mass head-on elastic collision transfers all KE to the stationary particle, so neutron KE becomes zero. For E > 20.4 eV, inelastic excitation is possible; the neutron does NOT necessarily stop. Statement A is correct: collision is elastic (not inelastic) for E < 20.4 eV.

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