Question

Calculate the number of atoms present per unit cell if product of density and volume of unit cell is 1.8 × 10\(^{-22}\) g. Mass of an atom = 4.5 × 10\(^{-23}\) g

• A. 2
• B. 4
• C. 6
• D. 8

Hint:

To calculate the number of atoms in a unit cell, divide the product of density and volume of the unit cell by the mass of a single atom.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The product of density (\( \rho \)) and volume (\( V \)) is the mass of one unit cell. We need to find the number of atoms (\( z \)) in that unit cell.
Step 2: Key Formula or Approach:
Mass of unit cell = \( z \times (\text{Mass of one atom}) \).
\[ z = \frac{\text{Mass of unit cell}}{\text{Mass of one atom}} \]
Step 3: Detailed Explanation:
Given:
Mass of unit cell (\( \rho \times V \)) = \( 1.8 \times 10^{-22} \text{ g} \)
Mass of one atom = \( 4.5 \times 10^{-23} \text{ g} \)
Calculate \( z \):
\[ z = \frac{1.8 \times 10^{-22}}{4.5 \times 10^{-23}} \] \[ z = \frac{18 \times 10^{-23}}{4.5 \times 10^{-23}} \] \[ z = \frac{18}{4.5} = 4 \] Step 4: Final Answer:
The number of atoms per unit cell is 4.