Q27 / 150 · MHT CET 2021 (24 Sep Shift 1) · Chemistry

An element is found to crystallize with BCC structure having density $8.55 \mathrm{~g} \mathrm{~cm}^{-3}$. What is the edge length of unit cell? (At. mass of element $=93$ )

  • Correct answer
    A
    $\left(3.61 \times 10^{-23}\right)^{1 / 3} \mathrm{~cm}$
  • B
    $\left(3.91 \times 10^{-20}\right)^{1 / 3} \mathrm{~cm}$
  • C
    $\left(3.01 \times 10^{-224}\right)^{1 / 3} \mathrm{~cm}$
  • D
    $\left(3.30 \times 10^{-20}\right)^{1 / 3} \mathrm{~cm}$

Solution

$\begin{aligned} & \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \\ & \mathrm{a}^3=\frac{\mathrm{ZM}}{\mathrm{d} \cdot \mathrm{N}_{\mathrm{A}}} \quad[\mathrm{Z}=2 \text { for } \mathrm{BCC}] \\ & =\frac{2 \times 93}{8.55 \times 6 \times 10^{23}} \\ & =3.61 \times 10^{-23} \\ & \mathrm{a}=\left(3.61 \times 10^{-23}\right)^{1 / 3} \mathrm{~cm}\end{aligned}$

Hence, the correct answer is option: 'A'.

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