JEE PYQ: Solid State Question 15
Question 15 - 2019 (08 Apr Shift 2)
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?
(1) 45%
(2) 75%
(3) 90%
(4) 65%
Show Answer
Answer: (3)
Solution
Volume occupied by atoms in solid 2 $= \dfrac{4}{3}\pi r^3 + \dfrac{4}{3}\pi(2r)^3 = 12\pi r^3$. Relationship between body diagonal and radius of atom ($r$): $6r = \sqrt{3},a$, so $a = \dfrac{6r}{\sqrt{3}}$. Packing efficiency $= \dfrac{\text{vol. of particles}}{\text{vol. of unit cell}} = \dfrac{12\pi r^3}{\left(\dfrac{6r}{\sqrt{3}}\right)^3} \times 100 = 90%$.
BETA
