A metal exists as FCC crystal. If the atomic radius is 100$\sqrt{2}$ pm and the density of metal is

Question

A metal exists as FCC crystal. If the atomic radius is 100$\sqrt{2}$ pm and the density of metal is 12,500 kg/m3, then the metal is (Atomic masses: Ca = 40, Co = 58.9, Sn = 119.8, Pb = 207.9 and NA = 6 × 1023)

Accepted Answer

$d = \frac{Z.M}{N_{A}.V} \Rightarrow 12.5\text{gm/c}\text{m}^{3} = \frac{4 \times M\text{gm}}{\left( 6 \times 10^{23} \right) \times \left( \frac{4 \times 100\sqrt{2} \times 10^{- 10}}{\sqrt{2}} \right)\text{c}\text{m}^{3}}$

$\therefore M = 120 \Rightarrow \text{Metal is Sn}$

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