An element with BCC structure has edge length of $500 \mathrm{pm}$. If its density is $4 \mathrm{~g}…

An element with BCC structure has edge length of $500 \mathrm{pm}$. If its density is $4 \mathrm{~g} \mathrm{~cm}^3$, find atomic mass of the element?
  1. $150 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $100 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $125 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $250 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & \mathrm{a}=500 \mathrm{pm}=500 \times 10^{-10} \mathrm{~cm} \\ & =5 \times 10^{-8} \mathrm{~cm} \\ & \mathrm{Z}=2(\text { for } \mathrm{BCC}) \\ & \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \\ & \mathrm{M}=\frac{\mathrm{d} \times \mathrm{N}_{\mathrm{A}} \times \mathrm{a}^3}{\mathrm{Z}}=\frac{4 \times 6.022 \times 10^{23} \times\left(5 \times 10^{-8}\right)^3}{2} \\ & \mathrm{M}=150 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 2)

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