Q38 / 180 · COMEDK 2018 · Chemistry

The radii of $\mathrm{Na}^{+}$and $\mathrm{Cl}^{-}$ions are 95 pin and 181 pm respectively. The edge length of $\mathrm{NaCl}$ unit cell is

  • A
    $276 \mathrm{pm}$
  • B
    $138 \mathrm{pm}$
  • Correct answer
    C
    $552 \mathrm{pm}$
  • D
    $415 \mathrm{pm}$

Solution

$\mathrm{NaCl}$ forms fec structure. $\therefore(\text { Diagonal length })^{2}=(\sqrt{2} a)^{2}=2\left(r^{+}\right)^{2}+2\left(r^{-}\right)^{2}$ Where, $a=$ edge length, $r^{+}$and $r^{-}$are radii of $\mathrm{Na}^{+}$and $\mathrm{Cl}^{-}$ions. $a=2\left[\left(r^{+}\right)^{2}+\left(r^{-}\right)^{2}\right]=2(95+181)=2 \times 276=552 \mathrm{pm}$

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

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