AMU 2026 — science PYQ

1. Concept of Body-Centered Cubic (BCC) Unit Cell

A Body-Centered Cubic (BCC) unit cell features atoms at specific geometric positions within its lattice structure:

• Atoms located at each of the $8$ corners of the cube.

• Exactly $1$ full atom located at the dead center of the cube body.

Since corner atoms are shared equally among $8$ adjacent unit cells, their fractional contribution inside a single cell is calculated as:

$$\text{Corner Contribution}=8\times \frac{1}{8}=1\text{ atom}$$

The central atom belongs exclusively to that specific cell:

$$\text{Body-Center Contribution}=1\times 1=1\text{ atom}$$

Therefore, the total effective number of atoms contained within a single BCC unit cell ($Z$) is:

$$Z=1+1=2\text{ atoms/unit cell}$$

2. Step-by-Step Calculation

We are given:

• Total number of atoms in the crystal crystal lattice = $8\times 10^{23}$ atoms

• Number of effective atoms per individual unit cell = $2$

To find the total number of unit cells present in the sample, divide the total number of atoms by the number of atoms contained per single unit cell:

$$\text{Number of Unit Cells}=\frac{\text{Total Number of Atoms}}{\text{Atoms per Unit Cell}}$$

$$\text{Number of Unit Cells}=\frac{8\times 10^{23}}{2}$$

$$\text{Number of Unit Cells}=4\times 10^{23}$$

Correct Answer

The correct option is (b) $4\times 10^{23}$.