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MHT CET · Chemistry · Solid State

Calculate the density of an element having molar mass \(63 \mathrm{~g} \mathrm{~mol}^{-1}\) that forms FCC structure \(\left[\mathrm{a}^3 \times \mathrm{N}_{\mathrm{A}}=28 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]\)

  1. A \(6.0 \mathrm{~g} \mathrm{~cm}^{-3}\)
  2. B \(\quad 9.0 \mathrm{~g} \mathrm{~cm}^{-3}\)
  3. C \(5.0 \mathrm{~g} \mathrm{~cm}^{-3}\)
  4. D \(7.0 \mathrm{~g} \mathrm{~cm}^{-3}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\quad 9.0 \mathrm{~g} \mathrm{~cm}^{-3}\)

Step-by-step Solution

Detailed explanation

For FCC lattice, \(n=4\)
\(\rho=\frac{\mathrm{M} \times \mathrm{n}}{\mathrm{a}^3 \times \mathrm{N}_{\mathrm{A}}}=\frac{63 \mathrm{~g} \mathrm{~mol}^{-1} \times 4}{28 \mathrm{~cm}^3 \mathrm{~mol}^{-1}}=9.0 \mathrm{~g} \mathrm{~cm}^{-3}\)