Question

Number of atom in per unit cell in B.C.C is:
(A) $9$
(B) $4$
(C) $2$
(D) $1$

Answer 1

Hint: B.C.C refers to a body centred cubic cell.
- A unit cell of crystalline solid is defined as the smallest repeating portion which shows the complete geometry of the crystalline substance or represents the arrangement of lattice points in crystalline lattice.


Complete Solution :
- A unit cell having a lattice point (constituent particle of crystalline solid) at the body centre in addition to the lattice point at every corner called body centred cubic cell. In B.C.C the central atom is surrounded by eight equidistant atoms.
- The total number of atom present in per unit cell of B.C.C type of crystalline solid-
\[\text{(}\dfrac{\text{1}}{\text{8}}\,\text{ }\!\!\times\!\!\text{ }\,\text{8)}\,\text{+}\,\text{(1 }\!\!\times\!\!\text{ 1)}\,\text{=}\,\,\text{1+1 = 2}\,\text{atom/unit}\,\text{cell}\]
In this case one atom lies at the each corner of the cube and that one atom contribute to eight adjacent unit cell, so the contribution of the eight corner atom in one unit cell$=\,(\dfrac{1}{8}\times 8)\,=\,1$
While one atom present in the centre of the unit cell hence total no of atom present in one unit cell = $\text{1+}\,\text{1}\,\text{= 2}\,\text{atom}$
So, the correct answer is “Option C”.

Additional information –
If we talk about the arrangement of particles in B.C.C the sphere is square and closely packed and is slightly open up. In the second layer the sphere at the top of the hollow space and the third layer are exactly over the first layer.
- In B.C.C the packing efficiency (total volume occupied by atom or ion) is 68%.

Note: Coordination number represents the number of nearest neighbouring particles around a specific particle in a given crystalline substance which is completely different with total number of atoms in a cell. The coordination number of the B.C.C crystalline unit cell is eight, while the number of unit cells is two.