Q4 / 90 · KVPY 2017 (19 Nov SB/SX) · Chemistry

Polonium (atomic mass = 209) crystallizes in a simple cubic structure with a density of $9.32 \mathrm{~g} \mathrm{~cm}^{-3}$. Its lattice parameter (in $\mathrm{pm}$ ) is closest to

  • A
    421
  • Correct answer
    B
    334
  • C
    481
  • D
    193

Solution

$\mathrm{d}=\frac{\mathrm{N} \times \mathrm{M}}{\mathrm{N}_{\mathrm{A}} \times \mathrm{a}^{3}}$ $9.32=\frac{1 \times 209}{6.023 \times 10^{23} \times \mathrm{a}^{3}}$ $\therefore \mathrm{a}^{3}=37.2 \times 10^{-24 \mathrm{~S}}$ $\mathrm{a}=3.33 \times 10^{-8} \mathrm{~cm}$ $\cong 334 \mathrm{pm}$

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

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