JEE Advanced · 2021 · 03 Oct 2021 · Paper 1 · Solid State

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For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction =

\frac{Packing efficiency}{100}

)

(A)0.74
(B)0.63✓ Correct
(C)0.52
(D)0.48

Answer: (B)

Solution

From the structure, there is 1 anion at the center and 3 cations at the corners (each shared by 4 unit cells, contributing 3/4 per cell). The cations occupy square planar voids, so

r_{+} / r_{-} = 0.414

. The edge length

a = 2 r_{-}

.

Packing fraction =

\frac{Volume of ions}{Volume of unit cell} = \frac{1 \times \frac{4}{3} π r _{-}^{3} + 3 \times \frac{4}{3} π r _{+}^{3}}{a ^{3}}

Substituting

r_{+} = 0.414 r_{-}

and

a = 2 r_{-}

:

P.F. =

\frac{\frac{4}{3} π ( r _{-}^{3} + 3 \times ( 0.414 ) ^{3} r _{-}^{3} )}{8 r _{-}^{3}} = \frac{π}{6} (1 + 3 \times 0.071) = \frac{π}{6} (1.213) \approx 0.63

JEE Advanced · 2021 · 03 Oct 2021 · Paper 1 · Single correct option

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JEE Advanced · 2021 · 03 Oct 2021 · Paper 1 · Solid State

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