The Spacing of the Atoms of a Crystal Is $159 \mathrm { pm }$

Multiple Choice

The spacing of the atoms of a crystal is $159 \mathrm { pm }$ . A monoenergetic beam of neutrons directed normally at the surface of the crystal undergoes first order diffraction at an angle of $58 ^ { \circ }$ from the normal. What is the energy of each of the neutrons? ( $m _ { \text {neutron } } = 1.675 \times 10 ^ { - 27 } \mathrm {~kg} , 1 \mathrm { eV } = 1.6 \times$ $\left. 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

A) $0.050 \mathrm { eV }$
B) $0.039 \mathrm { eV }$
C) $0.056 \mathrm { eV }$
D) $0.061 \mathrm { eV }$
E) $0.045 \mathrm { eV }$