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A metal crystallizes with a BCC lattice. Density is and atomic weight is . The length of the body diSolid State Chemistry Question

Question

A metal crystallizes with a BCC lattice. Density is $19.3 \text{ g/cm}^3$ and atomic weight is $183.9 \text{ g/mol}$. The length of the body diagonal of the unit cell is closest to:

Answer: A

💡 Solution & Explanation

For BCC, $Z=2$ and $\rho=\frac{ZM}{N_Aa^3}$. Thus $a^3=\frac{2\times183.9}{6.022\times10^{23}\times19.3}\text{ cm}^3$, giving $a\approx316\text{ pm}$. The body diagonal is $\sqrt{3}a\approx1.732\times316\approx547\text{ pm}$.

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