To solve this problem, we need to understand the structure of a copper unit cell. Copper has a face-centered cubic (FCC) structure.

1. For the [110] direction:

In a FCC structure, the [110] direction is along the face diagonal. The face diagonal of a cube is √2 times the edge length. Therefore, the length of the [110] direction in the unit cell is 3.61Å * √2 = 5.10Å.

In the [110] direction, there are two atoms along the face diagonal. Therefore, the number of atoms per unit length along the [110] direction is 2 atoms / 5.10Å = 0.392 atoms/Å.

2. For the [111] direction:

In a FCC structure, the [111] direction is along the body diagonal. The body diagonal of a cube is √3 times the edge length. Therefore, the length of the [111] direction in the unit cell is 3.61Å * √3 = 6.25Å.

In the [111] direction, there are three atoms along the body diagonal. Therefore, the number of atoms per unit length along the [111] direction is 3 atoms / 6.25Å = 0.48 atoms/Å.

Question

To solve this problem, we need to understand the structure of a copper unit cell. Copper has a face-centered cubic (FCC) structure.

1. For the [110] direction:

In a FCC structure, the [110] direction is along the face diagonal. The face diagonal of a cube is √2 times the edge length. Therefore, the length of the [110] direction in the unit cell is 3.61Å * √2 = 5.10Å.

In the [110] direction, there are two atoms along the face diagonal. Therefore, the number of atoms per unit length along the [110] direction is 2 atoms / 5.10Å = 0.392 atoms/Å.

2. For the [111] direction:

In a FCC structure, the [111] direction is along the body diagonal. The body diagonal of a cube is √3 times the edge length. Therefore, the length of the [111] direction in the unit cell is 3.61Å * √3 = 6.25Å.

In the [111] direction, there are three atoms along the body diagonal. Therefore, the number of atoms per unit length along the [111] direction is 3 atoms / 6.25Å = 0.48 atoms/Å.

Knowee AI · Accepted Answer

To solve this problem, we need to understand the structure of a copper unit cell. Copper has a face-centered cubic (FCC) structure.

1. For the [110] direction:

In a FCC structure, the [110] direction is along the face diagonal. The face diagonal of a cube is √2 times the edge length. Therefore, the length of the [110] direction in the unit cell is 3.61Å * √2 = 5.10Å.

In the [110] direction, there are two atoms along the face diagonal. Therefore, the number of atoms per unit length along the [110] direction is 2 atoms / 5.10Å = 0.392 atoms/Å.

2. For the [111] direction:

In a FCC structure, the [111] direction is along the body diagonal. The body diagonal of a cube is √3 times the edge length. Therefore, the length of the [111] direction in the unit cell is 3.61Å * √3 = 6.25Å.

In the [111] direction, there are three atoms along the body diagonal. Therefore, the number of atoms per unit length along the [111] direction is 3 atoms / 6.25Å = 0.48 atoms/Å.

Lattice constant of a copper unit cell is 3.61 A. Compute the density of atoms per unit length along direction[110] and [111].

Question

Lattice constant of a copper unit cell is 3.61 A. Compute the density of atoms per unit length along direction [110] and [111].

Solution

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