Iron crystallizes in a bcc system with a lattice parameter of 2.861 A . Calculate the density of iron in the bcc system ( atomic weight of Fe=56, Avogadros no. $= 6.02 \times 10^{23} m o l^{- 1})$

7.92 g m l^{- 1}

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8.96 g m l^{- 1}

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2.78 g m l^{- 1}

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6.72 g m l^{- 1}

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Solution

The correct option is A $7.92 g m l^{- 1}$
$a = s i d e l e n g h t o f B a a l l = 2.861 A$
$V o l u m e = a^{3} = 2.341 \times 10^{- 29}$
$m a s s = 24 \times 50 \times \frac{1}{N_{A}}$
$∴ d e n s i t y = \frac{m a s s}{v o l u m e} = \frac{24 \times 50 \times 1}{6 \times 10^{23} \times 2.341 \times 10^{- 29}}$
$= 7.94 \times 10^{6} g / m s^{2}$
$∴ d e n s i t y = 7.94 g m l^{- 1}$

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