Question

What is true about a bcc unit cell?
(This question has multiple correct options.)
Thus, following statements are correct:
A) The number of atoms in the unit cell is 2.
B) In addition to an atom at the centres of the body, in a unit cell, there are 8 atoms at 8 different corners.
C) One-eighth of an atom is at a corner of the unit cell.
D) None of these

Answer 1

Hint: Body-centered cubic cell or the BCC structure is a repeating unit in the crystal lattice structure. The body-centered unit cell is an advancement in the primitive cubic unit cell by adding one atom at the centre of the body. Eight atoms at the corner contribute $\text{ }\dfrac{1}{8}\text{ }$ to the total number of atoms per unit cell.

Complete Solution :
The unit cell is known as the smallest repeating unit in the crystal lattice.
Body centered cubic (BCC) lattice is a unit cell that has 8 atoms at the eight corners of the unit cell and one atom at the centre of the unit cell. The BCC unit cell has six cell parameters such as length a, b, and c and interfacial angles as $\text{ }\alpha \text{ }$ , $\text{ }\beta $ and $\text{ }\gamma \text{ }$ .
In BCC unit cell the unit cell parameters are $\text{ a = b = c }$ and the interfacial angles are equal to $\text{ }\alpha \text{ = }\beta \text{ = }\gamma \text{ = 9}{{\text{0}}^{\text{0}}}\text{ }$ .
The body-centered cubic structure is as shown below:

According to the lattice structure, it is clear that the central atom wholly belongs to the BCC unit cell. Thus it contributes 100 percent towards the cell.
Let's calculate the number of atoms present per unit cell. Here, each atom at the corner contributes $\text{ }\frac{1}{8}\text{ }$ towards the unit cell. There are a total of eight atoms in the unit cell. Thus the total number of atom present at the corner is,
$\text{ }\frac{1}{8}\text{ }\times \text{ 8 = 1 atom }$
The unit cell has one atom at the centre of the body. Thus the total number of atoms per BCC unit cell are, $\text{ 1 + 1 = 2 }$
The volume occupied by the atoms in the BCC unit cell is equal to the $\text{ 68}{\scriptstyle{}^{0}/{}_{0}}\text{ }$ .BCC structure has a coordination number equal to 8.

Thus, the following statements are correct:
A) The number of atoms in the unit cell is 2.
B) In addition to an atom at the centres of the body, in a unit cell, there are 8 atoms at 8 different corners.
C) One-eighth of an atom is at a corner of the unit cell.
So, the correct answer is “Option A, B and C”.

Note: some of the examples of metal which exhibit BCC structure are lithium, sodium, potassium, chromium, barium, vanadium, tungsten, etc. BCC structures are harder and less malleable than close-packed cubic structures. This is usually the high-temperature form of metal.