An element (atomic mass 100 g/mol) having bcc structure has a unit cell edge of 400 pm. Then the density of the element is

10.376 g/cm³

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5.188 g/cm³

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7.289 g/cm³

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2.144 g/cm³

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Solution

The correct option is D: 5.188 g/cm³
No.of atoms in BCC (z) =2
The atomic mass of an element (M) = 100 g/mol
Cell edge length(a) = 400pm = $400 \times 10^{- 10} c m$

$d = \frac{z \times M}{a^{3} \times N_{A}} = \frac{2 \times 100}{(400 \times 10^{- 10})^{3} \times (6.023 \times 10^{23})} = 5.188 g / c m$

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