JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Solid State

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The correct relationship between unit cell edge length 'a' and radius of sphere 'r' for face-centred and body centred cubic structures respectively are:

(A) $r = 22 a$ and $3 r = 4 a$
(B) $r = 22 a$ and $4 r = 3 a$
(C) $22 r = a$ and $4 r = 3 a$ ✓ Correct
(D) $22 r = a$ and $3 r = 4 a$

Answer: (C)

Solution

For FCC (face-centered cubic), atoms touch along the face diagonal:

2 a = 4 r

, which gives

a = 22 r

. For BCC (body-centered cubic), atoms touch along the body diagonal:

3 a = 4 r

. Therefore, the correct relationships are

22 r = a

(FCC) and

4 r = 3 a

(BCC).

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Single correct option

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