Solid State - Result Question 35
####35. A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of $400 pm$. If the density of the substance in the crystal is $8 g cm^{-3}$, then the number of atoms present in $256 g$ of the crystal is $N \times 10^{24}$. The value of $N$ is
(2017 Adv.)
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Answer:
Correct Answer: 35. (2)
Solution:
- Density $(\rho)=8=\frac{4 \times M}{N _A\left(4 \times 10^{-8} cm\right)^{3}}$
$$ \begin{gathered} \Rightarrow \quad M=128 \times 10^{-24} N _A \Rightarrow \quad \text { No of atoms }=\frac{256}{M} \times N _A \\ =\frac{256}{128 \times 10^{-24} N _A} \times N _A=2 \times 10^{24} \end{gathered} $$
