An element has a cubic structure with a cell edge of 288 pm. The density of the element is $7.2 g {cm}^{- 2}$ . 208 g of the element has $24.16 \times 10^{23}$ number of atoms. The unit cell of this cubic structure is

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face - centred

hexagonal

body - centred

primitive

answer is B.

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Detailed Solution

$a = 288 pm = 288 \times 10^{- 12} m = 2.88 \times 10^{- 8} cm$

$ρ = \frac{M \times Z}{a^{3} \times N_{0}} Z = \frac{7.2 g {cm}^{- 3} \times 24.16 \times 10^{23} \times {(2.88 \times 10^{- 8} cm)}^{3}}{208} = 1.99 \approx 2$

The unit cell is body centred.

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