An element crystallises in fcc type of unit cell. The volume of one unit cell is $24.99 \times 10^{-24}…

An element crystallises in fcc type of unit cell. The volume of one unit cell is $24.99 \times 10^{-24} \mathrm{~cm}^{3}$ and density of the element $7 \cdot 2 \mathrm{~g} \mathrm{~cm}^{-3} .$ Calculate the number of unit cells in $36 \mathrm{~g}$ of pure sample of element?
  1. $2 \cdot 0 \times 10^{23}$
  2. $2 \cdot 0 \times 10^{21}$
  3. $2 \cdot 0 \times 10^{24}$
  4. $1 \cdot 25 \times 10^{21}$

Solution

Vol. of element $=\frac{\text { Mass }}{\text { Density }}=\frac{36 \mathrm{~g}}{7.2 \mathrm{~g} \mathrm{~cm}^{-3}}=5 \mathrm{~cm}^{3}$ No. of unit cells in $36 \mathrm{~g}$ of pure sample of element $=\frac{\text { Total Vol. of element }}{\text { Vol. of one unit cell }}$ $=\frac{5 \mathrm{~cm}^{3}}{24.99 \times 10^{-24} \mathrm{~cm}^{3}}=2.0 \times 10^{23}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

Practice more Solid State questions on Aicharya