Question

Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 3.165 x 10-8 cm. The molar mass of tungsten is 183.84 grams/mole. 1 meter = 1012 picometers (a) What is the atomic radius of tungsten in picometers in this structure? (b) Calculate the density of tungsten i grams/cm3

Answer 1

(a) Atomic radius of tungsten,

$$    \begin{aligned}    \gamma &=\frac{\sqrt{3}}{4} \times \text { edge length }(a) \\    &=\frac{\sqrt{3}}{4} \times 3 \cdot 165 \times 10^{-10} \mathrm{~m} \times \frac{10^{12} \text { picorneter }}{1 \text { meter }}    \end{aligned}    $$

\(=137\) picometer

(b) Fro BCC, \(z=2\) atoms | unit cell

Molar mass of tungsten \(, M=183.84 \mathrm{~g} / \mathrm{mol}\).

\( N_{A}=6 \cdot 02 p \times 10^{23} \text { atoms } \mid \mathrm{mol} \)

\( d=\frac{z M}{a^{3} N_{A}} \)

\(d=\frac{2 \text{ atoms } \times 183.84 \mathrm{~g} / \mathrm{mol}}{(3.165 \times 10^{ -8})^{3} \times 6.022 \times 10^{23}\mathrm{~g} / \mathrm{mol}} \)

\(= 19.2 \mathrm{~g} / \mathrm{cm^{3}}\)

Density of tungsten is \(19 \cdot 2 \mathrm{~g} / \mathrm{cm}^{3}\).