Chemistry Q140 – AP-EAMCET 2026

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r

is the radius of a metal atom, then the total volume of atoms present in a body centered cubic cell of a metal is

Clue 1 of 3: Unit Cell Structure

Understand the arrangement of atoms in a Body-Centered Cubic (BCC) unit cell to determine the number of atoms it effectively contains.

🧠 Full Solution Path

Step 1: Determine the number of atoms per BCC unit cell✦ Active

A Body-Centered Cubic (BCC) unit cell has atoms located at all eight corners and one atom at its body center.

Each corner atom is shared by 8 unit cells, so its contribution to one unit cell is $\frac{1}{8}$ . For 8 corners, the total contribution from corner atoms is $8 \times \frac{1}{8} = 1$ atom.

The atom at the body center belongs entirely to that unit cell, contributing 1 atom.

Therefore, the total effective number of atoms ( $Z$ ) in a BCC unit cell is $1 + 1 = 2$ atoms.

💡 Teacher's Secret Hint

Always remember the effective number of atoms for common unit cell types: Simple Cubic ( $Z = 1$ ), BCC ( $Z = 2$ ), and FCC ( $Z = 4$ ). This is crucial for many solid-state calculations.

Step 2: Recall the formula for the volume of a single atom○ Expand

Assuming the atoms are spherical, the volume of a single atom ( $V_{a t o m}$ ) with radius $r$ is given by the formula:

V_{a t o m} = \frac{4}{3} π r^{3}

Step 3: Calculate the total volume of atoms in the BCC unit cell○ Expand

The total volume of atoms present in the BCC unit cell is the product of the effective number of atoms per unit cell ( $Z$ ) and the volume of a single atom ( $V_{a t o m}$ ).

V_{t o t a l} = Z \times V_{a t o m}

Substitute the values obtained from the previous steps:

V_{t o t a l} = 2 \times (\frac{4}{3} π r^{3})

V_{t o t a l} = \frac{8}{3} π r^{3}

This matches option 2.

💡 Teacher's Secret Hint

Ensure you distinguish between the volume of the unit cell itself ( $a^{3}$ ) and the total volume occupied by atoms within the unit cell. The question specifically asks for the latter.

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Chemistry Question 140 – AP-EAMCET 2026

Clue 1 of 3: Unit Cell Structure

🧠 Full Solution Path