Q.Explain how much portion of an atom located at

• Corner atom: shared equally among 8 unit cells, so only $\tfrac18$ belongs to a given cell and the remaining $\tfrac{7}{8}$ is part of the neighbouring unit cells. …

Step 1 – Corner atom.

In a cubic lattice each corner is the meeting point of 8 unit cells. An atom at a corner is therefore shared equally among 8 cells, contributing

Hence for any one cell, the fraction of the corner atom lying in the neighbouring cells is

Step 2 – Body-centre atom.

An atom at the body centre lies completely within a single unit cell and touches no other cell, so it contributes $1$ (whole atom) to its own cell and …

Use the sharing rule for cubic cells: a corner site is common to 8 cells (contribution $1/8$ each), a body-centre site to 1 cell only. The 'port …

• Saying a corner atom is shared by 4 cells (that is a 2-D layer / edge confusion); in 3-D a corner is shared by 8. …