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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')
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(Edge length is represented by 'a')
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Verified Answer
The correct answer is:
0.067 a
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.
$$
\therefore \quad \mathrm{r}_{\text {sphere }}=\frac{a-\frac{\sqrt{3}}{2} \mathrm{a}}{2}=\left(\frac{2-\sqrt{3}}{4}\right) \mathrm{a}=0.067 \mathrm{a}
$$
$$
\Rightarrow \mathrm{R}=\frac{\sqrt{3} \mathrm{a}}{4}
$$
$$
\therefore \text { Empty space at edge }=a-2 R=a-\frac{\sqrt{3} a}{2}
$$
$=$ diameter of sphere.
$$
\therefore \quad \mathrm{r}_{\text {sphere }}=\frac{a-\frac{\sqrt{3}}{2} \mathrm{a}}{2}=\left(\frac{2-\sqrt{3}}{4}\right) \mathrm{a}=0.067 \mathrm{a}
$$
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