Calculation of the number of atoms in a cubic based unit cell

To calculate the number of atoms in a cubic based unit cell, we need to consider the arrangement of atoms within the unit cell. In this case, we have one atom on each corner and two atoms on each of the body diagonals.

Arrangement of atoms in a cubic based unit cell

A cubic based unit cell consists of eight atoms, with one atom on each corner and six atoms on each face. In addition, there are two atoms located on each of the body diagonals.

Calculating the number of atoms

To calculate the number of atoms in a cubic based unit cell, we can follow these steps:

1. Count the number of atoms on the corners: Each corner atom is shared by eight unit cells, so we count each corner atom as 1/8th of an atom. Since there are eight corners in a cubic based unit cell, the total number of corner atoms is 8 x 1/8 = 1 atom.

2. Count the number of atoms on the body diagonals: Each body diagonal atom is shared by four unit cells, so we count each body diagonal atom as 1/4th of an atom. Since there are two body diagonals in a cubic based unit cell, the total number of body diagonal atoms is 2 x 1/4 = 1/2 atom.

3. Count the number of atoms on the faces: Each face atom is shared by two unit cells, so we count each face atom as 1/2 of an atom. Since there are six faces in a cubic based unit cell, the total number of face atoms is 6 x 1/2 = 3 atoms.

4. Calculate the total number of atoms: Add up the number of atoms from the corners, body diagonals, and faces. 1 (corner atom) + 1/2 (body diagonal atom) + 3 (face atoms) = 4.5 atoms.

Therefore, there are 4.5 atoms in a cubic based unit cell with one atom on each corner and two atoms on each of the body diagonals.

Explanation

In a cubic based unit cell, the arrangement of atoms is such that there is one atom on each corner and two atoms on each of the body diagonals. By considering the sharing of atoms between multiple unit cells, we can determine the total number of atoms in the unit cell. In this case, we find that there are 4.5 atoms in the unit cell.