Question
Find the volume occupied by a particle in a simple cubic unit cell if the radius of a particle in it is 190 pm.
MHT CET
Chemistry
Solid State
2026
MHT CET 2026 (17 April Shift 1)
MHT CET Chemistry Question (2026) — Solution
Options
- A. 6.410 10^ -23 \ cm ^3
- B. 3.625 10^ -23 \ cm ^3
- C. 5.715 10^ -23 \ cm ^3
- D. 2.873 10^ -23 \ cm ^3
Answer
D. 2.873 10^ -23 \ cm ^3
Step-by-step solution
The volume occupied by a particle is the volume of the spherical particle itself. Given the radius of the particle, r = 190 pm = 190 10^ -10 cm = 1.9 10^ -8 cm . Volume of one particle is given by: V = 4 3 r^3 Substituting the value of r: V = 4 3 3.1416 (1.9 10^ -8 cm )^3 V = 4.1888 6.859 10^ -24 cm ^3 V = 28.73 10^ -24 cm ^3 = 2.873 10^ -23 cm ^3 Answer: 2.873 10^ -23 \ cm ^3
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