Solid State - Result Question 43
####43. A metal crystallises into two cubic phases, face centred cubic (fcc) and body centred cubic (bcc), whose unit cell lengths are 3.5 and $3.0 \AA$, respectively. Calculate the ratio of densities of fcc and bcc.
(1999, 3M)
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Answer:
Correct Answer: 43. $(1.86 \AA)$
Solution:
- Density $\propto \frac{N}{a^{3}}$
$$ \Rightarrow \quad \frac{d _1}{d _2}=\frac{N _1}{N _2}\left(\frac{a _2}{a _1}\right)^{3}=\frac{4}{2}\left(\frac{3}{3.5}\right)^{3}=1.26 $$
