Question

What is the mass of an fcc unit cell if mass of one atom of an element is $6 \times 10^{-23$ g?}

• A. $24 \times 10^{-22}\ \text{g}$
• B. $4 \times 10^{-23}\ \text{g}$
• C. $2.4 \times 10^{-22}\ \text{g}$
• D. $2.4 \times 10^{-23}\ \text{g}$

Hint:

Remember: fcc unit cell always contains exactly 4 atoms.

Answer 1

The Correct Option is C

Step 1: Number of atoms in fcc unit cell.
A face centered cubic (fcc) unit cell contains 4 atoms per unit cell.

Step 2: Mass of one atom.
Mass of one atom is given as $6 \times 10^{-23}$ g.

Step 3: Calculate mass of unit cell.
\[ \text{Mass of unit cell} = 4 \times 6 \times 10^{-23} \] \[ = 24 \times 10^{-23} = 2.4 \times 10^{-22}\ \text{g} \]
Step 4: Conclusion.
Hence, the mass of one fcc unit cell is $2.4 \times 10^{-22}$ g.