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MHT CET · Chemistry · Solid State

A metal has BCC structure with edge length of unit cell \(400 \mathrm{pm}\). Density of metal is \(4 \mathrm{~g} \mathrm{~cm}^{-3}\) What is molar mass of metal?

  1. A \(40 \mathrm{~g} \mathrm{~mol}^{-1}\)
  2. B \(27 \mathrm{~g} \mathrm{~mol}^{-1}\)
  3. C \(92 \mathrm{~g} \mathrm{~mol}^{-1}\)
  4. D \(77 \mathrm{~g} \mathrm{~mol}^{-1}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(77 \mathrm{~g} \mathrm{~mol}^{-1}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \\ & \mathrm{a}=400 \mathrm{pm} \\ & =400 \times 10^{-10} \mathrm{~cm} \\ & =4 \times 10^{-8} \mathrm{~cm} \\ & \mathrm{Z}=2 \text { for BCC } \\ & 4=\frac{2 \times \mathrm{M}}{6.022 \times 10^{23} \times\left(4 \times 10^{-8}\right)^3} \\ & \mathrm{M}=\frac{4 \times 6.022 \times 10^{23} \times 64 \times 10^{-24}}{2} \\ & =77 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}\)
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