Calculate the density of each of the following metals from the data given: (a) aluminum, fcc structure, atomic radius 143 pm; (b) potassium, bcc structure, atomic radius 227 pm. Show all work!
Added by James W.
Step 1
Given: Atomic radius (r) = 143 pm = 143 x 10^-12 m For FCC structure, the atomic volume (V) = (4/3) * π * (r)^3 V = (4/3) * π * (143 x 10^-12)^3 V = (4/3) * π * (292187 x 10^-36) V = 404.5 x 10^-30 m^3 Show more…
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3. The atomic weight, density, and atomic radius for three hypothetical alloys are listed in the following table. For each, determine whether its crystal structure is FCC, BCC, or simple cubic. Show your work. Alloy amu (g/mol) 43.1 84.4 91.6 Density (g/cm³) 12.2 14.6 13.7 Radius (nm) 0.122 0.146 0.137
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Below are listed the atomic weight, density, and atomic radius for three hypothetical alloys. For each determine whether its crystal structure is FCC, BCC, or simple cubic and then justify your determination. A simple cubic unit cell is shown in Figure 3.23 $$\begin{array}{lccc} \hline & \text {Atomic} & & \text {Atomic} \\ & \text {Weight} & \text {Density} & \text {Radius} \\ \text {Alloy} & \text { (g/mol) } & \left(\mathrm{g} / \mathrm{cm}^{3}\right) & (\boldsymbol{n m}) \\ \hline \mathrm{A} & 43.1 & 6.40 & 0.122 \\ \mathrm{B} & 184.4 & 12.30 & 0.146 \\ \mathrm{C} & 91.6 & 9.60 & 0.137 \\ \hline \end{array}$$
Calculate the average density of a single Al-27 atom by assuming that it is a sphere with a radius of $0.143 \mathrm{nm}$. The masses of a proton, electron, and neutron are $1.6726 \times 10^{-24} \mathrm{~g}, 9.1094 \times 10^{-28} \mathrm{~g},$ and $1.6749 \times 10^{-24} \mathrm{~g},$ respec- tively. The volume of a sphere is $4 \pi r^{3} / 3,$ where $r$ is its radius. Express the answer in grams per cubic centimeter. The density of aluminum is found experimentally to be $2.70 \mathrm{~g} / \mathrm{cm}^{3} .$ What does that suggest about the packing of aluminum atoms in the metal?
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