The radius of the largest sphere which fits properly at the centre of the edge of body centred cubic unit cell is: (Edge length is represented by 'a') :

Question

The radius of the largest sphere which fits properly at the centre of the edge of body centred cubic unit cell is: (Edge length is represented by 'a') : (A) 0.134 a (B) 0.027 a (C) 0.067 a (D) 0.047 a

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/4e140fef341b6d483e09f41edb18c0b6-.png" /> a = 2(R + r) (a/2) =(R+r) .....(1) a√3 =4R .....(2) Using (1) (2) (a/2) = (a√3/4) =r a((2-√3/4))=r r=0.067 a

Q. The radius of the largest sphere which fits properly at the centre of the edge of body centred cubic unit cell is : (Edge length is represented by 'a') :

0.134 a

0.027 a

0.067 a

0.047 a

$a = 2 (R + r)$

$\frac{a}{2} = (R + r)$ .....(1)

$a 3 = 4 R$ .....(2)

Using (1) & (2)

$\frac{a}{2} = \frac{a 3}{4} = r$

$a (\frac{2 - 3}{4}) = r$

$r = 0.067 a$

Q. The radius of the largest sphere which fits properly at the centre of the edge of body centred cubic unit cell is : (Edge length is represented by 'a') :

0.134 a

0.027 a

0.067 a

0.047 a

a=2(R+r) 2a​=(R+r) .....(1) a3​=4R .....(2) Using (1) & (2) 2a​=4a3​​=r a(42−3​​)=r r=0.067a

$a = 2 (R + r)$

$\frac{a}{2} = (R + r)$ .....(1)

$a 3 = 4 R$ .....(2)

Using (1) & (2)

$\frac{a}{2} = \frac{a 3}{4} = r$

$a (\frac{2 - 3}{4}) = r$

$r = 0.067 a$