JEE Main 2019 — Chemistry solution

JEE Main2019Chemistry

Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?

A
45%
B
65%
C
75%
D
90%

Solution

Volume occupied by atoms in solid 2

$= \frac{4}{3} π r^{3} + \frac{4}{3} π (2r)^{3} = 12 π r^{3}$

relationship between edge length (a) and radius of atom (r)

$= 6r = 3 a \Rightarrow a = \frac{6r}{3}$

packing efficiency = $\frac{12 π r ^{3}}{( \frac{6 r}{3} ) ^{3}} \times 100 = 90%$

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