What is the formula for calculating the number of atoms in a face-centered cubic

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Question: What is the formula for calculating the number of atoms in a face-centered cubic unit cell? (2022)

Options:

Correct Answer: N = 4

Exam Year: 2022

Solution:

In a face-centered cubic unit cell, there are 4 atoms (1/8 from each of the 8 corners and 1/2 from each of the 6 faces).

What is the formula for calculating the number of atoms in a face-centered cubic unit cell? (2022)

What is the formula for calculating the number of atoms in a face-centered cubic unit cell? (2022)

Step 1: Understand that a face-centered cubic (FCC) unit cell has atoms at its corners and faces.
Step 2: Identify that there are 8 corners in a cube.
Step 3: Each corner atom is shared by 8 adjacent unit cells, so each corner contributes 1/8 of an atom to the unit cell.
Step 4: Calculate the contribution from the corners: 8 corners * 1/8 atom per corner = 1 atom from corners.
Step 5: Identify that there are 6 faces on a cube.
Step 6: Each face atom is shared by 2 adjacent unit cells, so each face contributes 1/2 of an atom to the unit cell.
Step 7: Calculate the contribution from the faces: 6 faces * 1/2 atom per face = 3 atoms from faces.
Step 8: Add the contributions from corners and faces: 1 atom (from corners) + 3 atoms (from faces) = 4 atoms in total.

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