Calculate the density of an element having molar mass $63 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms FCC…

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. $6.0 \mathrm{~g} \mathrm{~cm}^{-3}$
  2. $\quad 9.0 \mathrm{~g} \mathrm{~cm}^{-3}$
  3. $5.0 \mathrm{~g} \mathrm{~cm}^{-3}$
  4. $7.0 \mathrm{~g} \mathrm{~cm}^{-3}$

Solution

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

Asked in: MHT CET 2024 (03 May Shift 1)

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