QJEEM20Chdc6f: JEE Main 2020 Chemistry - Class 12 JEEM20Chdc6f Solution: An element with molar mass 2.7 × 10 -2 kg mol -1 forms a cubic…

Molar mass of an element (M) = 27 gm mol^–1

Edge length of a cubic unit cell (a) = 405 pm = 4.05 × 10^–8 cm

density of the element (d) = 2.7 gm/cc

d = $$\frac{Z\times M}{N_A\times {\left(a\right)}^3}$$

$$\Rightarrow$$ 2.7 = $$\frac{Z\times 27}{6\times {10}^{23}\times {\left(4.05\times {10}^{-8}\right)}^3}$$

$$\Rightarrow$$ Z = 4

The element has fcc unit cell

$$\therefore$$ $$\sqrt{2}$$a = 4r

$$\Rightarrow$$ r = $$\frac{1.414\times 405}{4}$$

= 143 pm

= 143 × 10^–12 m