Question

Choose the correct statment(s) regarding a unit cell:

• A. A particle at body-centre is shared by 8 other unit cells.
• B. A particle at body-centre is shared by no other unit cell.
• C. A particle present at the edge-centre is shared by four-unit cells.
• D. A particle present at the edge-centre is shared by six-unit cells.

Answer 1

Answer: (B), (C)

A particle present at the edge-centre is shared by four-unit cells.

Contribution of Body-Centred Particles:
A particle at body-centre is shared by no other unit cell.
It contributes fully to the unit cell as shown :


Contribution of Edge-Centred Particles:
A particle present at the edge-centre is shared by four-unit cells.


Contributes $\frac{1}{4}$ part to the unit cell as shown :

Theory :
Effective number of Particles $\left(Z_{eff}\right)$ in a unit cell:
$Z_{eff}=(n_c\times \frac{1}{8})+(n_f\times \frac{1}{2})+(n_b\times \frac{1}{1})+(n_e\times \frac{1}{4})$
where
$n_c=\text{no. of particles at corners of a unit cell}$
$n_f=\text{no. of particles at face-centre of a unit cell}$
$n_b=\text{no. of particles at body-centre of a unit cell}$
$n_e=\text{no. of particles at edge-centre of a unit cell}$