The Solid State

Short Answer Type

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How many atoms can be assigned to its unit cell if an element forms
(i) a body centred cubic cell, and (ii) a face centred cubic cell?

Body centre wholly belongs to the unit cell in which it is present. Thus
in a body-centered cubic (bcc) unit cell:
(i) 8 corners × 1/8per corner atom= 8 x 1/8 = 1 atom
(ii) 1 body centre atom = 1 × 1 = 1 atom
∴ Total number of atoms per unit cell = 2 atoms
For face centred 

(i) 8 corners atoms × 1/8 atom per unit cell
= 8  x1/8 = 1 atom

(ii) 6 face-centred atoms ×1/2 atom per unit cell = 6 ×1/2 = 3 atoms
∴ Total number of atoms per unit cell = 4 atoms

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