Question

A crystalline solid substance has a density of $ 10\text{ }g/c{{m}^{3}} $ and the length of the edge of the unit cell (FCC) is $ \text{2}\text{.0}\overset{\text{o}}{\mathop{\text{A}}}\,. $ How many number of atom are present in 200 g of the solid?

• A. $ 2\times {{10}^{23}} $
• B. $ 1\times {{10}^{26}} $
• C. $ 1\times {{10}^{25}} $
• D. $ 5\times {{10}^{27}} $

Answer 1

Answer: (C)

Given, edge of the unit cell $ \text{= 2}\text{.0}\overset{\text{o}}{\mathop{\text{A}}}\, $ $ =2.0\times {{10}^{-8}}\,cm $ $ \therefore $ $ {{a}^{3}}=8\times {{10}^{-24}}cm $ Density of crystal, $ d=\frac{Z\times M}{{{a}^{3}}.{{N}_{0}}} $ (Where, Z = number of atoms per unit cell = 4 for fee, M = molecular mass) $ \Rightarrow $ ` $ 10=\frac{4\times M}{(8\times {{10}^{-24}})(6.023\times {{10}^{23}})} $ $ M=\frac{10\times 8\times 6.023}{10\times 4} $ $ =12.046 $ Number of atoms of solid in 200 g $ =\frac{200}{12.046}\times 6.023\times {{10}^{23}} $ $ =16.60\times 6.023\times {{10}^{23}}=1\times {{10}^{25}} $