Question:
A diatomic molecule $X_{2}$ has a body-centred cubic (bcc) structure with a cell edge of $300\, pm$. The density of the molecule is $6.17 \,g \,cm ^{-3}$. The number of molecules present in $200\, g$ of $X _{2}$ is (Avogadro constant $\left.\left( N _{ A }\right)=6 \times 10^{23} \,mol ^{-1}\right)$
A diatomic molecule $X_{2}$ has a body-centred cubic (bcc) structure with a cell edge of $300\, pm$. The density of the molecule is $6.17 \,g \,cm ^{-3}$. The number of molecules present in $200\, g$ of $X _{2}$ is (Avogadro constant $\left.\left( N _{ A }\right)=6 \times 10^{23} \,mol ^{-1}\right)$
Updated On: Jul 6, 2024
- $8\, N _{ A }$
- $40\, N _{ A }$
- $4 \,N _{ A }$
- $2 \,N _{ A }$
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The Correct Option is C
Solution and Explanation
$p =\frac{2 \times \frac{ M }{ N _{ A }}}{ a ^{3}}$
$ \Rightarrow 6.17=\frac{2 \times \frac{ M }{ N _{ A }}}{\left(3 \times 10^{-8} cm \right)^{3}}$
$\Rightarrow M \simeq 50 gm / mol$
No $=\frac{ w }{ M } \times N _{ A }=\frac{200}{50} \times N _{ A }=4 N _{ A }$
$ \Rightarrow 6.17=\frac{2 \times \frac{ M }{ N _{ A }}}{\left(3 \times 10^{-8} cm \right)^{3}}$
$\Rightarrow M \simeq 50 gm / mol$
No $=\frac{ w }{ M } \times N _{ A }=\frac{200}{50} \times N _{ A }=4 N _{ A }$
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Concepts Used:
Solid State
Solids are substances that are featured by a definite shape, volume, and high density. In the solid-state, the composed particles are arranged in several manners. Solid-state, in simple terms, means "no moving parts." Thus solid-state electronic devices are the ones inclusive of solid components that don’t change their position. Solid is a state of matter where the composed particles are arranged close to each other. The composed particles can be either atoms, molecules, or ions.
Types of Solids:
Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;
- Amorphous solids behave the same as super cool liquids due to the arrangement of constituent particles in short-range order. They are isotropic and have a broad melting point (range is about greater than 5°C).
- Crystalline solids have a fixed shape and the constituent particles are arranged in a long-range order.