Q21 / 160 · TS EAMCET 2022 (20 Jul Shift 1) · Chemistry

$\mathrm{KBr}$ has rock salt type structural arrangements and has a density of $3.70 \mathrm{~g} / \mathrm{cm}^3$. The edge length of the unit cell is approximately [molecular weight of $\mathrm{KBr}=120 \mathrm{~g} / \mathrm{mol}$ ]

  • A
    $3 \times 10^{-8} \mathrm{~cm}$
  • B
    $12 \times 10^{-8} \mathrm{~cm}$
  • C
    $9 \times 10^{-8} \mathrm{~cm}$
  • Correct answer
    D
    $6 \times 10^{-8} \mathrm{~cm}$

Solution

$\mathrm{KBr}$ has fcc type structural arrangement. $\therefore \quad$ Effective no. of atoms (z) in a unit cell $=4$ $$ \begin{array}{ll} \therefore & \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \mathrm{a}^3} \text { where } \mathrm{a}=\text { the edge length } \\ \therefore & \mathrm{a}^3=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \mathrm{d}}=\frac{4 \times 120}{6.023 \times 10^{23} \times 3.7} \mathrm{~cm}^3 \\ \therefore & \mathrm{a}=6 \times 10^{-8} \mathrm{~cm} \end{array} $$

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

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