Q7 / 90 · JEE Main 2019 (11 Jan Shift 2) · Chemistry

The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by 'a')

  • A
    0.027 a
  • B
    0.047 a
  • C
    $0.134 \mathrm{a}$
  • Correct answer
    D
    0.067 a

Solution

For bcc $$ \Rightarrow \mathrm{R}=\frac{\sqrt{3} \mathrm{a}}{4} $$ $$ \therefore \text { Empty space at edge }=a-2 R=a-\frac{\sqrt{3} a}{2} $$ $=$ diameter of sphere. $$ \therefore \quad \mathrm{r}_{\text {sphere }}=\frac{a-\frac{\sqrt{3}}{2} \mathrm{a}}{2}=\left(\frac{2-\sqrt{3}}{4}\right) \mathrm{a}=0.067 \mathrm{a} $$

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

Relevant Questions