1. Magnesium has a hexagonal close packed (HCP) crystal structure with a c/a ratio of 1.624. The density of Mg is 1.74 g/cm³ and its atomic weight is 24.305 amu. Using only these data, compute the metallic radius of Mg.
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First, we need to find the lattice parameters of the hexagonal unit cell. The c/a ratio is given as 1.624, which means that the height (c) of the unit cell is 1.624 times the length of the side (a). Show more…
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Magnesium has an HCP crystal structure, a $c / a$ ratio of $1.624,$ and a density of $1.74 \mathrm{g} / \mathrm{cm}^{3}$ Compute the atomic radius for $\mathrm{Mg}.$
Metallic magnesium has a hexagonal close-packed structure and a density of $1.74 \mathrm{~g} / \mathrm{cm}^{3}$. Assume magnesium atoms to be spheres of radius $r$. Because magnesium has a close-packed structure, $74.1 \%$ of the space is occupied by atoms. Calculate the volume of each atom; then find the atomic radius, $r$. The volume of a sphere is equal to $4 \pi r^{3} / 3$.
Some hypothetical metal has the simple cubic crystal structure shown in Figure $3.23 .$ If its atomic weight is $74.5 \mathrm{g} / \mathrm{mol}$ and the atomic radius is $0.145 \mathrm{nm},$ compute its density.
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