Q.1 (v) The relation between edge length and radius for body centered cubic structure is –
A. \(r = \dfrac{a}{2}\)
B. \(r = \sqrt{3}\,\dfrac{a}{4}\)
C. \(r = \sqrt{2}\,\dfrac{a}{4}\)
D. \(r = \sqrt{3}\,\dfrac{a}{2}\)
Best answer
Answer: B. \(r = \sqrt{3}\,\dfrac{a}{4}\)
Answer: (b) \(r = \sqrt{3}\,\dfrac{a}{4}\)
In a bcc unit cell the atoms touch along the body diagonal, whose length is \(\sqrt{3}a\). The body diagonal contains \(4r\) (radius of two corner atoms plus the diameter of the body-centre atom): \(4r = \sqrt{3}a\), so \(r = \dfrac{\sqrt{3}a}{4}\).
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