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A neutron moving with some kinetic energy makes a head-on collision with a stationary hydrogen atom in its ground state. Assume the neutron and hydrogen atom have equal mass. Which of the following statements is/are correct?

1. If the kinetic energy of the neutron is less than 20.4 eV, the collision must be elastic
2. If the kinetic energy of the neutron is less than 20.4 eV, the collision may be inelastic
3. Inelastic collision can occur only when the initial kinetic energy of the neutron exceeds 20.4 eV
4. A perfectly inelastic collision is not possible between the neutron and the hydrogen atom

Correct answer: If the kinetic energy of the neutron is less than 20.4 eV, the collision must be elastic

Solution

For equal masses, only half the lab kinetic energy is available in the center-of-mass frame. The minimum excitation energy of hydrogen is 10.2 eV (n=1 to n=2). So at least 20.4 eV of lab-frame kinetic energy is needed for inelastic collision. Below 20.4 eV, the collision must be elastic. A perfectly inelastic collision would require the neutron to stick to the H atom, which does not happen physically here.

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