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Q.

Potassium crystallizes in body centered cubic lattice, with a unit cell length of 5.0 $\overset{\circ}{A}$ . When the metal is melted, the density of molten metal is found to be $0.9 g / c m^{3}$ . The percentage of empty space in the molten metal is nearly $(A t o m i c m a s s o f K = 39, N_{A} = 6 \times 10^{23})$

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a

41

b

32

c

68

d

59

answer is D.

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Detailed Solution

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Fractional space occupied by atoms $= \frac{V_{a t o m s}}{V_{l i q u i d}} = \frac{V_{a t o m s / m o l}}{V_{l i q u i d / m o l}}$
$= \frac{(6 \times 10^{23}) \times \frac{4}{3} π \times (\frac{\sqrt{3} \times 5 \times 10^{- 8}}{4})}{(39 / 0.9)} = 0.5883$
Percentage of empty space = (1 – 0.5883) $\times$ 100 = 41.17%

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