Answer
See in below
Work Step by Step
If the kinetic energy is not conserved, some kinetic energy of the neutrons should be used to excite the hydrogen atom. The least energy required to excite the hydrogen atom is the difference between the first excited state $(n = 2)$ and the ground state $(n = 1)$.
$E_2-E_1=[-\frac{13.6}{n_2^2}-(-\frac{13.6}{n_1^2})]\;eV
\\=[-\frac{13.6}{2^2}-(-\frac{13.6}{1^2})]\;eV\\
=10.2\;eV$
But the kinetic energy of the neutron is $6.0\;eV$, which is less than the value of $E_2-E_1$
Therefore, the collision must be elastic.
