Barium metal crystallizes in a body-centered cubic lattice with barium atoms only at the lattice point. If the density of barium metal is $3.50 g / {cm}^{3}$ , what is e length of the unit cell?

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$4.02 \times 10^{- 8} cm$

$3.19 \times 10^{- 8} cm$

$5.07 \times 10^{- 8} cm$

$6.39 \times 10^{- 8} cm$

answer is C.

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Detailed Solution

Barium atom $B \cdot C \cdot C \Rightarrow z = 2$

$\begin{array}{l} d = 3 .50 g / {cm}^{3} \\ N_{A} = 6 \times 10^{23} \\ M \cdot M \cdot of Ba = 137 g \end{array}$

a = length of unit cell

$\begin{array}{r} 350 = \frac{2 \times 137}{a^{3} \times 6 \times 1 b^{23}} \\ a^{3} = \frac{137 \times 2}{3 .5 \times 6 \times 10^{23}} \\ a = 5 .07 \times 10^{- 8} cm \end{array}$

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