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MHT CET · Chemistry · Solid State

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 \(=93\) )

  1. A \(\left(3.61 \times 10^{-23}\right)^{1 / 3} \mathrm{~cm}\)
  2. B \(\left(3.91 \times 10^{-20}\right)^{1 / 3} \mathrm{~cm}\)
  3. C \(\left(3.01 \times 10^{-224}\right)^{1 / 3} \mathrm{~cm}\)
  4. D \(\left(3.30 \times 10^{-20}\right)^{1 / 3} \mathrm{~cm}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(3.61 \times 10^{-23}\right)^{1 / 3} \mathrm{~cm}\)

Step-by-step Solution

Detailed explanation

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