JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Solid State

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

a

(A) $0.0027 a$
(B)0.047 a
(C)00137 a
(D) $0.07 a$ ✓ Correct

Answer: (D)

Solution

In a body-centred cubic cell the atoms touch along the body diagonal,

3 a = 4 R

, so

R = \frac{3 a}{4}

. A sphere of radius

r

sitting at the centre of an edge, between two corner atoms, satisfies

2 (R + r) = a

along that edge. Substituting

R

\frac{3 a}{2} + 2 r = a

, so

2 r = a (1 - \frac{3}{2})

and

r = \frac{( 2 - 1.732 ) a}{4} \approx 0.067 a \approx 0.07 a

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option

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