Metal $\mathrm{M}$ crystallizes into a fcc lattice with the edge length of $4.0 \times 10^{-8} \mathrm{~cm}$. The atomic mass of the metal is ____________ $\mathrm{g} / \mathrm{mol}$. (Nearest integer)
$\left(\right.$ Use : $\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-1}$, density of metal, $\mathrm{M}=9.03 \mathrm{~g} \mathrm{~cm}^{-3}$ )
Answer (integer)
87
Solution
$\rho=\frac{Z M}{N_{A} a^{3}} \Rightarrow M=\frac{9.03 \times 6.02 \times 10^{23} \times\left(4 \times 10^{-8}\right)^{3}}{4}$
<br/><br/>
$$
\begin{aligned}
&=\frac{9.03 \times 6.02 \times 64 \times 10^{-1}}{4} \\\\
&=86.9 \mathrm{~g} \mathrm{~mol}^{-1} \\\\
&\approx 87 \mathrm{~g} \mathrm{~mol}^{-1}
\end{aligned}
$$
About this question
Subject: Chemistry · Chapter: States of Matter · Topic: Gas Laws
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