A neutron and a ground-state hydrogen atom approach head-on with equal speeds and almost equal masses. Find minimum kinetic energy (eV, nearest integer) of each particle so an inelastic collision can excite hydrogen.
Physics · Mixed Chapter
JEE Main Practice

Question

A neutron and a ground-state hydrogen atom approach head-on with equal speeds and almost equal masses. Find minimum kinetic energy (eV, nearest integer) of each particle so an inelastic collision can excite hydrogen.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — First excitation from ground state of hydrogen requires 10.2 eV. Step 2 — Neutron and H atom have nearly equal masses and approach with opposite velocities of equal magnitude; laboratory centre of mass is stationary. Step 3 — The available collision energy is sum of their kinetic energies = 2K, where K is kinetic energy of each. Step 4 — Threshold is 2K = 10.2 eV ⇒ K = 5.1 eV; nearest integer = 5.