MHT CET202522 Apr 2025Evening ShiftChemistrySolid StateActual
Calculate the volume occupied by a particle in fcc unit cell if volume of unit cell is 1.6 10⁻²³ ~cm ^3
Options
- A5.44 10⁻²⁴ ~cm ^3
- B2.96 10⁻²⁴ ~cm ^3
- C8.37 10⁻²⁴ ~cm ^3
- D6.15 10⁻²⁴ ~cm ^3
Correct answer
B. 2.96 10⁻²⁴ ~cm ^3
Step-by-step solution
An FCC unit cell contains 4 atoms, with contributions of 1 from corners and 3 from face centers. The packing efficiency for FCC is 0.74, so the volume occupied by all atoms is 0.74 1.6 10⁻²³ = 1.184 10⁻²³ cm ^3 . Each particle occupies 1.184 10⁻²³ 4 = 2.96 10⁻²⁴ cm ^3 . The correct option is B .