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Number of atom per unit cell in B.C.C.

Asked in CBSE AIPMT 2002 · Unit cells and lattice parameters

(1) 9
(2) 4
(3) 2
(4) 1

Answer: (3) 2

Step-by-step solution

Idea: an atom at a corner is shared by the eight cells meeting there, so it contributes 1/8 to each; an atom at the body centre belongs to that cell alone.

Corner contribution: 8×1/8=1.

Body centre contribution: 1.

Total per unit cell: 1+1=2.

Why the other options are wrong

(1) 9 counts the eight corner atoms whole plus the body centre, forgetting that each corner is shared between eight neighbouring cells.
(2) 4 is the count for a face-centred cubic cell, not a body-centred one.
(4) 1 is the count for a simple cubic cell, which has corners only and no body centre.

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