A) \[\frac{\sqrt{3}}{2}\,a\]
B) \[\sqrt{2}a\]
C) \[\frac{a}{\sqrt{2}}\]
D) \[\frac{a}{2}\]
Correct Answer: A
Solution :
In a bcc structure, the position vectors of the nearest neighbours of the origin are \[\left( \pm \frac{a}{2}\hat{i}\pm \frac{a}{2}\hat{j},\,\pm \frac{a}{2}\,\hat{k} \right)\] The distance between any two nearest neighbours is \[\sqrt{{{\left( \frac{a}{2} \right)}^{2}}+{{\left( \frac{a}{2} \right)}^{2}}+{{\left( \frac{a}{2} \right)}^{2}}}=\sqrt{\frac{3{{a}^{2}}}{4}}\,\] \[=\frac{\sqrt{3}}{2}\,a\]
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