A diatomic molecule

Question:

A diatomic molecule $\mathrm{X}_{2}$ has a body-centred cubic $(b c c)$ structure with a cell edge of $300 \mathrm{pm}$. The density of the molecule is $6.17 \mathrm{~g} \mathrm{~cm}^{-3}$. The number of molecules present in $200 \mathrm{~g}$ of $X_{2}$ is :

(Avogadroconstant $\left.\left(\mathrm{N}_{\mathrm{A}}\right)=6 \times 10^{23} \mathrm{~mol}^{-1}\right)$

  1. $40 \mathrm{~N}_{\mathrm{A}}$

  2. $8 \mathrm{~N}_{\mathrm{A}}$

  3. $4 \mathrm{~N}_{\mathrm{A}}$

  4. $2 \mathrm{~N}_{\mathrm{A}}$


Correct Option: , 3

Solution:

For $b c c, Z=2$

$d=\frac{Z \times M}{N_{A} \times(a)^{3}}$

$\Rightarrow 6.17=\frac{2 \times M}{6.0 \times 10^{23} \times\left[3 \times 10^{-8}\right]^{3}}$

$\Rightarrow 6.17=\frac{2 \times M}{6.0 \times 2.7} \Rightarrow M=50$

No. of mole $=\frac{200}{50}=4$

No. of molecules $=4 N_{A}$.

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