Question

Certain quantity of metal is crystallised $60\%$ in ccp structure $40\%$ in hcp structure. What is the ratio of number of unit cells in ccp and hcp?

• A. $3:2$
• B. $1:1$
• C. $9:4$
• D. $4:9$

Answer 1

The correct option is C $9:4$

Let number of moles of metal crystallized= $n$

Number of moles crystallized in $ccp=n\times \frac{60}{100}=0.6n$

Number of moles crystallized in $hcp=n\times \frac{40}{100}=0.4n$

as $1$ unit of $ccp$ contains= $4$ atoms of metal or $\frac{4}{N_a}$ moles of metal

Thus $0.6n$ moles contains= $\frac{0.6n\times N_a}{4}$ unit cell of $ccp$

Similarly, $1$ unit cell of $hcp$ contains= $6$ atoms of metal or $\frac{6}{N_a}$ moles of metal.

Thus $0.4n$ moles contains= $\frac{0.4n\times N_a}{6}$ unit cell of $hcp$

Thus ratio of number of unit cell of $ccp$ and $hcp$ is

$R=\frac{\text{unit cell of ccp}}{\text{unit cell of hcp}}$

$=\frac{\frac{0.6\times n\times N_a}{4}}{\frac{0.4n\times N_a}{6}}=\frac{9}{4}$

So, the ratio is $9:4$