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Chemistry · Solid State

JEE Advanced 2021 — Paper 1 — Question 13

For the given close packed structure of a salt made of cation X\mathbf{X} and anion Y\mathbf{Y} shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction = packing   efficiency 100=\frac{\text { packing\; efficiency }}{100} )

Question figure
  1. Option A:

    0.74

  2. Option B:

    0.63

    Correct
  3. Option C:

    0.52

  4. Option D:

    0.48

Answer: B

Step-by-step solution

Packing fraction (f)=3×43πr+3+1×43πr−3a3(\mathrm{f})=\frac{3 \times \frac{4}{3} \pi \mathrm{r}_{+}^{3}+1 \times \frac{4}{3} \pi \mathrm{r}_{-}^{3}}{\mathrm{a}^{3}}

=1×43π[3(r+r)3+1](ar−)3=\frac{1\times\frac{4}{3}\pi\left[3\left(\frac{r_{+}}{r_{}}\right)^{3}+1\right]}{\left(\frac{a}{r_{-}}\right)^{3}}

Now 2r_ = a ∴ar−=2\therefore \frac{\mathrm{a}}{\mathrm{r}_{-}}=2 Also, r+r−=0.414\frac{r_{+}}{r_{-}}=0.414

So, f=→1×43×3.14[3×(0.414)3+1]f=\xrightarrow{1 \times \frac{4}{3} \times 3.14\left[3 \times(0.414)^{3}+1\right]}

(2)3(2)^{3} =0.634≈0.63=0.634 \approx 0.63

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2021
Paper
Paper 1
Subject
Chemistry
Chapter
Solid State
Topic
Types of Crystal Packing: SC, BCC, FCC, Hexagonal