A monoenergetic neutron beam passes through a hydrogen-like gas (not hydrogen) in the ground state. Collisions excite the ions and six spectral lines are emitted, one having wavelength (6200/51) nm. Find the minimum neutron kinetic energy in the form 25α × 10⁻² eV and determine α. Assume neutron and proton masses are nearly equal.
Physics · Atomic Structure and X-rays
JEE Mains Advanced

Question

A monoenergetic neutron beam passes through a hydrogen-like gas (not hydrogen) in the ground state. Collisions excite the ions and six spectral lines are emitted, one having wavelength (6200/51) nm. Find the minimum neutron kinetic energy in the form 25α × 10⁻² eV and determine α. Assume neutron and proton masses are nearly equal.

Physics · Atomic Structure and X-rays

G1 Physics · Accepted Answer

Six spectral lines imply excitation to n=4. The given wavelength identifies the hydrogen-like ion and the required excitation energy. Because the neutron and ion have comparable masses, the threshold projectile energy includes recoil. Carrying out the level-energy and collision-threshold calculation gives α=255.