question_answer

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) [JEE  Main Online Paper (Held on 11-jan-2019 Evening)]

A) 0.027 a                       

B) 0.134 a

C) 0.047 a           

D)   0.067 a

Correct Answer: D

Solution :

\[a=2(R+r)\Rightarrow \frac{a}{2}=(R+r)\]                                  ?(i) For\[bcc,\sqrt{3}a=4R\]                          ?(ii) Using (i) and (ii) \[\frac{a}{2}=\frac{a\sqrt{3}}{4}+r\Rightarrow r=\frac{a}{2}-\frac{a\sqrt{3}}{4}=a\left( \frac{2-\sqrt{3}}{4} \right)\] \[r=0.067a\]