Q90 / 200 · NEET 2008 (Screening) · Chemistry

If ' $a$ ' stands for the edge length of the cubic systems : simple cubic, body centred cubic and face centred cubic, then the ratio of radii of the spheres in these systems will be respectively,

  • Correct answer
    A
    $\frac{1}{2} a : \frac{\sqrt{3}}{4} a: \frac{1}{2 \sqrt{2}} a$
  • B
    $\frac{1}{2} a: \sqrt{3} a: \frac{1}{\sqrt{2}} a$
  • C
    $\frac{1}{2} a: \frac{\sqrt{3}}{2} a: \frac{\sqrt{2}}{2} a$
  • D
    $1 a: \sqrt{3} a: \sqrt{2} a$

Solution

For simple cubic, $\begin{aligned} \therefore & a & =2 r \\ \therefore & r & =\frac{a}{2} \end{aligned}$ For body centred cubic, $\begin{aligned} & a=\frac{4 r}{\sqrt{3}} \\ & r=\frac{\sqrt{3} a}{4} \end{aligned}$ For face centred cubic, $\begin{aligned} & a=2 \sqrt{2} r \\ & r=\frac{a}{2 \sqrt{2}} \end{aligned}$ Hence, the ratio of radii in simple cubic, body centred cubic and face centred cubic is $\frac{a}{2}: \frac{\sqrt{3} a}{4}: \frac{a}{2 \sqrt{2}}$

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

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