JEE Advanced 2021 · Paper 1 · Chemistry Q3

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ChemistrySingle correct+3 / -1Question 22 of 57

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

A cubic unit cell with the ions of one face drawn: four large anions Y touching along the face, at the corners of the face, and a smaller cation X at the centre of that face, fitting in the gap between them (the Y ions touch the X ion).

0.74

0.63

0.52

0.48

Answer and worked solution

Official answer: B

Read the structure. The anions Y sit at the cube corners and touch along each edge, so $a=2r_Y$ . The cation X sits at each face centre and touches the corner anions along the face diagonal:
$\sqrt2a=2r_Y+2r_X\implies r_X=(\sqrt2-1)r_Y\approx0.414\,r_Y.$

Contents of the cell. 1 Y (8 corners × $\frac18$ ) and 3 X (6 faces × $\frac12$ ).

Packing fraction.
$\frac{\frac43\pi\left(r_Y^3+3r_X^3\right)}{(2r_Y)^3}=\frac{4\pi}{3}\cdot\frac{1+3(0.414)^3}{8}=\frac{4.189\times1.213}8\approx0.63.$
(B)

Topics:Packing efficiency Crystal lattices and unit cells

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JEE Advanced 2021 · Paper 1, Chemistry question 3