A metal M crystallizes into two lattices :- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of $2.0$ and $2.5\,\mathop A\limits^o$ respectively. The ratio of densities of lattices fcc to bcc for the metal M is ____________. (Nearest integer)
Answer (integer)
4
Solution
$\begin{aligned} & d_1 \text {, Density of fcc lattice of metal } M=\frac{4 \times M}{N_0\left(a_{\mathrm{fcc}}\right)^3} \\\\ & d_2 \text {, Density of bcc lattice of metal } M=\frac{2 \times M}{N_0\left(a_{\mathrm{bcc}}\right)^3} \\\\ & \frac{d_1}{d_2}=\frac{4}{2}\left(\frac{a_{\mathrm{bcc}}}{a_{\mathrm{fcc}}}\right)^3=2\left(\frac{2.5}{2}\right)^3=3.90 \simeq 4\end{aligned}$
About this question
Subject: Chemistry · Chapter: States of Matter · Topic: Gas Laws
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