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Q.

If number of nearest neighbours, next nearest (2nd nearest) neighbour and next to next nearest (3rd nearest) neighbours are x, y and z respectively for body centered cubic unit cell. then calculate value of $\frac{xy}{z}$ .

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answer is 4.

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Detailed Solution

Unit cell = 8 cubes

Nearest neighbours $\Rightarrow \frac{\sqrt{3} a}{2}$

Next nearest neighbours = a

Next to next nearest neighbours = $\sqrt{2 a}$

$x = 8; y = 6; z = 12$

$\frac{xy}{z} = \frac{8 \times 6}{12} = 4$

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