JEE Main & Advanced
JEE Main Paper (Held On 11-Jan-2019 Evening)
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) \[\frac{a}{2}=\frac{a\sqrt{3}}{4}+r\Rightarrow r=\frac{a}{2}-\frac{a\sqrt{3}}{4}=a\left( \frac{2-\sqrt{3}}{4} \right)\] \[r=0.067a\]