Question

Gold crystallises in fcc centred cubic structure. If atomic mass of gold is $197gmo{l}^{-1}$, the mass of the unit cell of gold will be:

• A. $3.25\times {10}^{-23}Kg$
• B. $6.5\times {10}^{-23}Kg$
• C. $3.9\times {10}^{-24}Kg$
• D. $1.3\times {10}^{-24}Kg$

Answer 1

Answer: (D)

$1.3\times {10}^{-24}Kg$

Atomic mass of gold is 197 g/mol. 1 mole of gold weighs 197 g. 1 mole of gold contains $6.023\times {10}^{23}$ atoms. Hence, $6.023\times {10}^{23}$ atoms of gold weighs 197 g. 1 atom of gold weighs $\frac{197g}{6.023\times {10}^{23}atoms}$
A fcc unit cell of gold contains 4 atoms.

The mass of the unit cell of gold $=$ mass of 4 atoms of gold
$=\frac{197g}{6.023\times {10}^{23}atoms}\times 4atoms=1.3\times {10}^{-21}g$.

Convert the unit from g to Kg.

The mass of the unit cell of gold $=1.3\times {10}^{-21}g\times \frac{1kg}{1000g}=1.3\times {10}^{-24}Kg$.