Solid State - Result Question 6

####6. 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 ‘) (2019 Main, 11 Jan II)

(a) 0.134a

(b) 0.027a

(c) 0.047a

(d) 0.067a

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Answer:

Correct Answer: 6. (d)

Solution:

  1. For body centred cubic bcc structure,

radius (R)=34a

Where, a= edge length

According to question, the structure of cubic unit cell can be shown as follows:

a=2(R+r)

On substituting the value of R from Eq. (i) to Eq. (ii), we get

a2=34a+r

r=a234a=2a3a4 r=a(23)4 r=0.067a



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