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Potassium has a body-centred cubic structure with the nearest neighbour distance 452 pm. Its relative atomic mass is 39. Its density would be

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$0.81 g {cm}^{- 3}$

$0.91 g {cm}^{- 3}$

$0.71 g {cm}^{- 3}$

$1.01 g {cm}^{- 3}$

answer is C.

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Detailed Solution

$ρ = \frac{N M}{a^{3} N_{A}} = \frac{(2) (29 g {mol}^{- 1})}{{(2 \times 452 \times 10^{- 12} m / \sqrt{3})}^{3} (6.022 \times 10^{23} {mol}^{- 1})} = 9.11 \times 10^{5} {gm}^{- 3} = 0.91 g {cm}^{- 3}$

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