Question

If the aluminum unit cell exhibits face-centered behavior then how many unit cells are present in 54g of aluminum?

• A. $3.011\times {10}^{23}$
• B. $1.204\times {10}^{24}$
• C. $5.575\times {10}^{21}$
• D. $2.408\times {10}^{22}$

Answer 1

The correct option is A $3.011\times {10}^{23}$

$\text{Atomic mass of Al = 27g/mole (contains}6.022\times {10}^{23}\text{Al atoms})$
In FCC, there are 4 Al atoms per unit cell.
If 27 g Al contains $6.022\times {10}^{23}$ Al atoms then 54 g Al contains $1.2044\times {10}^{24}$atoms.
Thus, if 1 unit cell contains 4 Al atoms then number of unit cells containing $1.2044\times {10}^{24}$ atoms =$\frac{1.2044\times {10}^{24}\times 1}{4}=3.011\times {10}^{23}$ unit cells.