Number of atoms per unit area of the plane (010) in a simple cubic crystal:

The (010) plane of a simple cubic crystal refers to a plane that is perpendicular to the crystallographic axis labeled as 'b' and parallel to the other two axes labeled as 'a' and 'c'. In order to determine the number of atoms per unit area of this plane, we need to consider the arrangement of atoms in a simple cubic crystal structure.

Simple cubic crystal structure:

In a simple cubic crystal structure, the atoms are arranged in a regular pattern where each atom is located at the corners of a cube. The atoms are not present in the center of the cube or on any face diagonals. The unit cell of a simple cubic crystal structure consists of one atom.

Calculating the number of atoms per unit area:

To calculate the number of atoms per unit area of the (010) plane, we need to consider the arrangement of atoms in the crystal structure and the area of the plane.

1. Determine the area of the (010) plane:
- The (010) plane is parallel to the 'a' and 'c' axes, so its area is given by the product of the lengths of these two axes, denoted as A = a * c.

2. Determine the number of atoms in the unit cell:
- In a simple cubic crystal structure, there is only one atom per unit cell. Therefore, the number of atoms in the unit cell is 1.

3. Determine the number of unit cells in the (010) plane:
- Since the (010) plane is parallel to the 'a' and 'c' axes, the number of unit cells in this plane is equal to the number of unit cells along these axes.
- The number of unit cells along the 'a' axis is given by n_a = a / a, where a is the length of the 'a' axis.
- The number of unit cells along the 'c' axis is given by n_c = c / c, where c is the length of the 'c' axis.

4. Determine the number of atoms per unit area:
- The total number of atoms in the (010) plane is given by the product of the number of atoms in the unit cell and the number of unit cells in the plane, denoted as N = 1 * n_a * n_c.
- The number of atoms per unit area of the (010) plane is then given by the ratio of the total number of atoms to the area of the plane, denoted as N/A = N / A.

Summary:

In summary, the number of atoms per unit area of the plane (010) in a simple cubic crystal can be determined by calculating the area of the plane, determining the number of atoms in the unit cell, determining the number of unit cells in the plane, and finally calculating the ratio of the total number of atoms to the area of the plane.