An element (atomic mass = $100 g / m o l e$ ) having $B C C$ structure has an edge length of $400 p m$ . The density of the element is (no. of atoms in $B C C_{Z} = 2$ ).

2.144 g / c m^{3}

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5.2 g / c m^{3}

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7.289 g / c m^{3}

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10.376 g / c m^{3}

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Solution

The correct option is B $5.2 g / c m^{3}$
Mass of a unit cell $= \frac{Z \times M}{N_{A}}$
Z is the number of atoms per unit cell which is 2 for BCC
M is the molar mass of the atom = 100 g/mol
$N_{A}$ is avagadro number
Volume of the unit cell $= a^{3}$
Here, a is the edge length = 400 pm
Density of a unit cell is given by
$ρ = \frac{Z \times M}{N_{A} \times a^{3}}$
i.e $ρ = \frac{2 \times 100}{6 \times 10^{23} \times (400 \times 10^{- 10})^{3}}$ = $5.2 g / c m^{3}$

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