First slide

Crystal lattices and unit cells

Question

Sodium (Na = 23) crystallizes in bcc arrangement with the interfacial separation between the atom at the edge 53.6 pm. The density of sodium crystal is:

Moderate

A

2.07 g/cc
B

2.46 g/cc
C

1.19 g/cc
D

2.23 g/cc

Solution

$\begin{array}{l} a - 2 r = 53 .6 pm \\ also 4 r = \sqrt{3} a \\ \Rightarrow a - \frac{\sqrt{3}}{2} a = 53 .6 \\ \Rightarrow a = \frac{53 .6 \times 2}{2 - \sqrt{3}} = 400 pm \\ Density (ρ) = \frac{2 \times 23}{6 .023 \times 10^{23} \times 4^{3} \times 10^{- 24}} \\ = 1 .19 g / cc \end{array}$

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