Question
A metal has a fcc structure if the edge length of unit cell is 200 pm, calculate the volume occupied by particles in a unit cell.
MHT CET
Chemistry
Solid State
2026
MHT CET 2026 (20 April Shift 2)
MHT CET Chemistry Question (2026) — Solution
Options
- A. 2.08 10^ -24 \ cm ^3
- B. 5.92 10^ -24 \ cm ^3
- C. 8 10^ -24 \ cm ^3
- D. 3.14 10^ -24 \ cm ^3
Answer
B. 5.92 10^ -24 \ cm ^3
Step-by-step solution
Edge length of the unit cell, a = 200 pm = 2 10^ -8 cm Volume of the unit cell, V = a^3 = (2 10^ -8 )^3 = 8 10^ -24 cm ^3 For a face-centered cubic (fcc) structure, the packing efficiency is 74\%. Volume occupied by particles in the unit cell = 0.74 V = 0.74 8 10^ -24 cm ^3 = 5.92 10^ -24 cm ^3 Answer: 5.92 10^ -24 \ cm ^3
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