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  4. 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') :

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Q. 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') :

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Solution:

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$a = 2\left(R + r\right) $

$\frac{a}{2} =\left(R+r\right)$ .....(1)

$ a\sqrt{3} =4R $ .....(2)

Using (1) & (2)

$ \frac{a}{2} = \frac{a\sqrt{3}}{4} =r$

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

$ r=0.067\, a $