Question

What is the diameter of the largest sphere that will fit in the void at the centre of the cube edge of a BCC crystal of edge length a ?

• A. 0.134 a
• B. 0.76 A
• C. 0.05548 a
• D. 0.098 a

Answer 1

Answer: (A)

0.134 a

Answer 2

x = $\sqrt{\frac{a^{2}}{4} + \frac{a^{2}}{4}} = \sqrt{\frac{a^{2}}{2}} = \frac{a}{\sqrt{2}}$

The atom present in the void will touch the atom at the corner at first

\ r_x + r = a/2 ; 4r = $\sqrt{3}$a or r = $\frac{\sqrt{3}a}{4}$

\ r_x = $\frac{a}{2}$–$\frac{\sqrt{3}a}{4}$ = $\frac{2a}{4}$–$\frac{\sqrt{3}a}{4}$ = $\frac{a}{4}$ (2–$\sqrt{3}$)

= 0.067 a

\ 2r_x = 2 × 0.067a = 0.134 a.