The total number of atoms in body centred cubic unit cell (bcc) is

2

The correct answer is option 1. 2.

So, first of all, let us discuss closed-packed structures. We should know that the closed-packed structure refers to the most tightly packed structure. We should know that the unit cell is the most basic, occupies the very least volume, and is the repeating structure of any solid. We should know that we assume atoms as spherical. This explains the bonding and structures of metallic crystals. These spherical particles can be packed into different arrangements. In closest packed structures, the arrangements of the spheres are densely packed in order to take up the greatest amount of space possible.

Now, we will calculate the number of atoms in each type of unit cell.

First, we will take a simple cubic unit cell. We should know that 8 atoms are located on 8 corners of the lattice. Each atom contributes \((\frac{1}{8})\) of the original volume of the cell. So, we can say that: 8× \(\frac{1}{8}\) \(= 1 \text{ atom}\)

There is one atom in a simple cubic unit cell.

In the same way, we will calculate atoms for body-centered cubic. There are 8 corners and 1 corner shares 1/8th the volume of the entire cell, so:

\(8 × \frac{1}{8}\) \(= 1\text{ atom}\)
There is also 1 atom at the center of the body of the cube. This can’t be shared. So, it will stay as one atom whole: \(1 × 1 = 1\text{ atom}\)
Total atoms \(= 1 + 1 = 2 \text{ atoms}\)
So, from this, we can say that the number of atoms in the unit cell of the body-centered cubic crystal is 2.