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Question

Choose the correct statment regarding a unit cell:

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

The correct option is C A particle at body-centre is shared by no other unit cell.
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 14 part to the unit cell as shown :

Theory :
Effective number of Particles (Zeff) in a unit cell:
Zeff=(nc×18)+(nf×12)+(nb×11)+(ne×14)
where
nc= no. of particles at corners of a unit cell
nf= no. of particles at face-centre of a unit cell
nb= no. of particles at body-centre of a unit cell
ne= no. of particles at edge-centre of a unit cell

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