ï»¿ Explain how much portion of an atom located at (i) corner and (ii) body-centre of a cubic unit cell is part of its neighbouring unit cell. from Chemistry The Solid State Class 12 Nagaland Board

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Explain how much portion of an atom located at (i) corner and (ii) body-centre of a cubic unit cell is part of its neighbouring unit cell.

(i) Primitive cubic unit cell has atoms only at its corner. Each atom at a corner is shared between eight adjacent unit cells . four unit cells in the same layer and four unit cells of the upper (or lower) layer Therefore only 1/8th of an atom (molecule or ion) actually belongs to a particular unit cell.
since each cubic unit cell has 8 atoms on its corners, the total number of atoms in one unit cell is  atom.
(ii) The atom at the 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${×}{1}{/}{8}$ per corner atom =
(ii) 1 body centre atom =${1}{×}{1}{=}{1}$
therefore total number of atom per unit cell =2 atom.

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