question_answer

The first three nearest neighbor distance for primitive cubic lattice are respectively (edge length of unit cell = a):

A) \[a,\,\sqrt{2}a,\sqrt{3}a\]

B) \[\sqrt{3}a,\,\sqrt{2}a,\,a\]

C) \[a,\,\sqrt{2}a,2\,a\]

D) \[a,\,\sqrt{3}a,2\,a\]

Correct Answer: A

Solution :

[a]

\[AB=a\]           (Nearest)

\[BD=\sqrt{2}a\]            (Next-nearest)

\[CE=\sqrt{3}a\]            (Next-next-nearest)