An element crystallises bcc type of unit cell, the density and edge length of unit cell is $4 \mathrm{~g}…

An element crystallises bcc type of unit cell, the density and edge length of unit cell is $4 \mathrm{~g} \mathrm{~cm}^{-3}$ and 500 pm respectively. What is the atomic mass of an element?
  1. $125 \cdot 5$
  2. $100 \cdot 1$
  3. $250 \cdot 0$
  4. $150 \cdot 0$

Solution

In bcc, $\mathrm{n}=2, \rho=4 \mathrm{~g} \mathrm{~cm}^{-3}$ $\mathrm{a}=500 \mathrm{pm}=500 \times 10^{-10} \mathrm{~cm}=5 \times 10^{-8} \mathrm{~cm}$ $\therefore$ Volume of unit cell, $\mathrm{a}^{3}=\left(5 \times 10^{-8} \mathrm{~cm}\right)^{3}=125 \times 10^{-24} \mathrm{~cm}^{3}$ Now, $\mathrm{M}=\frac{\rho \times \mathrm{a}^{3} \times \mathrm{N}_{\mathrm{A}}}{\mathrm{n}}=\frac{4 \times 125 \times 10^{-24} \times 6.022 \times 10^{23}}{2}=150.5 \mathrm{~g} \mathrm{~mol}^{-1}$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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