Question

A crystalline solid substance has a density of $10g/c{m}^3$ and the length of the edge of the unit cell (FCC) is $\text{2}\text{.0}\stackrel{\text{o}}{A}.$ 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 $\text{= 2}\text{.0}\stackrel{\text{o}}{A}$ $=2.0\times {10}^{-8}cm$ $\therefore$ $a^3=8\times {10}^{-24}cm$ 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 $=\frac{200}{12.046}\times 6.023\times {10}^{23}$ $=16.60\times 6.023\times {10}^{23}=1\times {10}^{25}$