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A metal crystallises into simple, body centred and face centred cubic structure, whose unit cell lengths are*A*1, *A*2 and*A*3 respectively. The correct order of lengths of the unit cells is:

A)

*A*1* < A*2* < A*3

B)

*A*2 < *A*3 < *A*1

C)

*A*1 < *A*3 < *A*2

D)

*A*3 < *A*1 <* A*2

PLEASE EXPLAIN THIS

The correct option is (A).

Explanation:

The following formula will show, radius (r) is related to the unit cell length (a).

For BCC: a = sqrt(16/3)r {sqrt = square root}

For FCC: a = sqrt(8)r

For SC: a = 2r

Therefore, FCC will have largest unit length and SC (simple cubic) have the lowest.

Order of unit length (a) is:

$FCC>BCC>SC$

Regards.

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