Q: An element occuring in the bcc structure has 12.08 × 10^23 unit cells. The total number of atoms of the element in these cells will be

Explanation:
In a body-centered cubic (bcc) crystal structure, each unit cell contains a specific number of atoms. Here’s how to determine the total number of atoms given the number of unit cells:

1. Understand the BCC Structure:

– In a bcc structure, there are atoms at each of the eight corners of the cube and one atom in the center of the cube.
– Each corner atom is shared among eight adjacent unit cells. Therefore, each corner contributes 1/8 of an atom to a single unit cell.
– There are 8 corner atoms, so their total contribution is 8 × (1/8) = 1 atom.
– The center atom is entirely within the unit cell, contributing 1 full atom.
– Total atoms per unit cell in BCC = 1 (from corners) + 1 (center) = 2 atoms.

2. Calculate the Total Number of Atoms:

– Given the number of unit cells is 12.08 × 10²³.
– Since each unit cell has 2 atoms, multiply the number of unit cells by 2.
– Total atoms = 12.08 × 10²³ unit cells × 2 atoms/unit cell = 24.16 × 10²³ atoms.

Therefore, the total number of atoms in 12.08 × 10²³ unit cells of a bcc structure is 24.16 × 10²³.