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MHT CET 202625 AprilMorning Shift
Exam
MHT CET
Year
2026
Date
25 April
Shift
Morning Shift
Subject
Chemistry
Chapter
Solid State

MHT CET 2026 · 25 April · Morning Shift · Chemistry · Solid State

Which of the following formulae is used to find total volume of...

Which of the following formulae is used to find total volume of atoms present in face-centred cubic unit cell?

Options

  1. A203πr3\dfrac{20}{3}\pi r^3
  2. B243πr3\dfrac{24}{3}\pi r^3
  3. C123πr3\dfrac{12}{3}\pi r^3
  4. D163πr3\dfrac{16}{3}\pi r^3

Correct answer

D. 163πr3\dfrac{16}{3}\pi r^3

Step-by-step solution

In a face-centred cubic (fcc) unit cell, the total number of atoms per unit cell is Z=4Z = 4.

Assuming each atom is a sphere of radius rr, the volume of one atom is 43πr3\dfrac{4}{3}\pi r^3.

Total volume of atoms present in the fcc unit cell =Z×43πr3= Z \times \dfrac{4}{3}\pi r^3.

Total volume =4×43πr3=163πr3= 4 \times \dfrac{4}{3}\pi r^3 = \dfrac{16}{3}\pi r^3.

Answer: 163πr3\dfrac{16}{3}\pi r^3
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