Single Choice

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

A$$0.134 a$$
B$$0.027 a$$
C$$0.067 a$$
Correct Answer
D$$0.047 a$$

Solution

$$a = 2(R + r)$$

$$\dfrac{a}{2} = (R + r) $$

$$a \sqrt{3} = 4R$$

Using (1) & (2)

$$\dfrac{a}{2} = \dfrac{a \sqrt{3}}{4} +r$$

$$a \left(\dfrac{2 - \sqrt{3}}{4} \right) = r$$

$$r = 0.067 a$$

SIMILAR QUESTIONS

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