A neutron with a kinetic energy of 12.5 eV strikes a stationary hydrogen atom. Neglecting the mass difference between the neutron and the hydrogen atom, and assuming the neutron's line of motion remains unchanged, determine the possible kinetic energies of the neutron following the collision.

Step-by-step solution

Let the mass of the neutron and the hydrogen atom be m . Initial kinetic energy of the neutron, K = 12.5 eV . The maximum energy that can be lost in the collision occurs when the collision is perfectly inelastic. Maximum loss in kinetic energy, K_ max = 1 2 v_ rel ^2 = 1 2 ( m m m + m ) v^2 = 1 2 ( 1 2 m v^2 ) = K 2 K_ max = 12.5 2 = 6.25 eV The minimum energy required to excite a hydrogen atom from its ground state ( n=1 ) to the first excited state ( n=2 ) is 13.6 eV (1 - 1 4 ) = 10.2 eV . Since the maximum avail