A metal crystallises into simple, body centred and face centred cubic structure, whose unit cell lengths areA1, A2 andA3 respectively - Chemistry - The Solid State

Question

A metal crystallises into simple, body centred and face centred
cubic structure, whose unit cell lengths areA1,
A2 andA3 respectively The correct order of
lengths of the unit cells is:

A)
A1 < A2 < A3

B)
A2 < A3 < A1

​ C)
A1 < A3 < A2

​
D)
A3 < A1 < A2

PLEASE EXPLAIN THIS

​

Deepak Singh · Accepted Answer

Dear student,

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

A metal crystallises into simple, body centred and face centred cubic structure, whose unit cell lengths areA1, A2 andA3 respectively. The correct order of lengths of the unit cells is: A) A1 < A2 < A3 B) A2 < A3 < A1 ​ C) A1 < A3 < A2 ​ D) A3 < A1 < A2 PLEASE EXPLAIN THIS ​

A metal crystallises into simple, body centred and face centred cubic structure, whose unit cell lengths areA1, A2 andA3 respectively. The correct order of lengths of the unit cells is:

A)
A1 < A2 < A3

B)
A2 < A3 < A1

C)
A1 < A3 < A2

D)
A3 < A1 < A2

PLEASE EXPLAIN THIS