 Solution

ID: past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2021/1/b/solution

λ = \frac{h}{2 m _{n} E} = \frac{6.62607015 \times 1 0 ^{- 34}}{2 ( 1.67493 \times 1 0 ^{- 27} ) ( 25 \times 1 0 ^{- 3} ) ( 1.602176634 \times 1 0 ^{- 19} )} = 0.180891 nm .

2 d sin θ = λ

. The measured total deflection is

2 θ

, 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

d_{1} = 0.42457 nm, d_{2} = 0.29995 nm, d_{3} = 0.24462 nm, d_{4} = 0.21203 nm .

The last digits give the numerical calculation, rather than accuracy beyond the supplied angular precision.

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