Question

What is the mass of the unit cell of gold if it crystallizes in fcc structure?

• A. \( 98.14 \times 10^{-23} \, g \)
• B. \( 32.71 \times 10^{-23} \, g \)
• C. \( 65.42 \times 10^{-23} \, g \)
• D. \( 130.85 \times 10^{-23} \, g \)

Hint:

In fcc structures, the number of atoms per unit cell and the molar mass are crucial to determining the mass of the unit cell.

Answer 1

The Correct Option is D

Step 1: Understanding the fcc structure.
In the fcc (face-centered cubic) structure, there are 4 atoms per unit cell. The formula for the mass of the unit cell is: \[ \text{Mass of unit cell} = \frac{\text{Mass of 1 mole of gold}}{\text{Avogadro's number}} \times \frac{\text{Atoms per unit cell}}{4} \] Given that the molar mass of gold is 197 g/mol, the mass of the unit cell is calculated as: \[ \text{Mass of unit cell} = \frac{197}{6.022 \times 10^{23}} \times 4 = 130.85 \times 10^{-23} \, g \] Step 2: Analyzing the options.
(A) \( 98.14 \times 10^{-23} \, g \): Incorrect. This is not the correct mass.
(B) \( 32.71 \times 10^{-23} \, g \): Incorrect. This is too small.
(C) \( 65.42 \times 10^{-23} \, g \): Incorrect. This is not the correct mass.
(D) \( 130.85 \times 10^{-23} \, g \): Correct — This is the correct mass of the unit cell of gold in fcc structure.
Step 3: Conclusion.
The correct answer is (D) \( 130.85 \times 10^{-23} \, g \).