= Solution
{c}
The <neutron> is nonrelativistic at this <kinetic energy>. Its <de Broglie wavelength> is
$$
\lambda=\frac{h}{\sqrt{2m_nE}}
=\frac{6.62607015\times10^{-34}}{\sqrt{2(1.67493\times10^{-27})(25\times10^{-3})(1.602176634\times10^{-19})}}
=0.180891\,\mathrm{nm}.
$$
In <elastic scattering>, <Bragg's law> gives $2d\sin\theta=\lambda$. The measured total deflection is $2\theta$, so it must be halved before taking the sine. The reflection order is absorbed into the <Miller indices> of the diffracting <lattice planes>. In the order of the four measured rings, the <interplanar spacings> are
$$
\boxed{d_1=0.42457\,\mathrm{nm},\quad d_2=0.29995\,\mathrm{nm},\quad d_3=0.24462\,\mathrm{nm},\quad d_4=0.21203\,\mathrm{nm}.}
$$
The last digits give the numerical calculation, rather than accuracy beyond the supplied angular precision.
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