What portion of the volume of each atom or ion on the face of a unit cell is actually within the unit cell
1/2
1/4
3/4
all of it
none of it
1/2
The portion of the volume of each atom or ion within the unit cell depends on its position. Based on typical arrangements in a crystal lattice, the options are as follows:
1. 1/2: This is true for atoms or ions that are located on the face of the unit cell but are shared with adjacent unit cells. In this case, only half of the volume of the atom or ion lies within the unit cell.
2. 1/4: This is true for atoms or ions that are located on the corner of the unit cell but are shared with multiple adjacent unit cells. In this case, only one-fourth of the volume of the atom or ion lies within the unit cell.
3. 3/4: This is true for atoms or ions that are located on the face of the unit cell and are fully contained within the unit cell. In this case, three-quarters of the volume of the atom or ion lies within the unit cell.
4. All of it: This is true for atoms or ions that are located entirely within the unit cell, such as those at the center or within the body of the unit cell. In this case, the entire volume of the atom or ion lies within the unit cell.
5. None of it: This is not applicable for atoms or ions within the unit cell itself. All atoms or ions within the unit cell will have some portion of their volume within the unit cell.
Therefore, the correct answer depends on the specific arrangement and location of the atom or ion within the unit cell.
To determine the portion of the volume of each atom or ion on the face of a unit cell that is actually within the unit cell, we need to consider the atomic positions within the unit cell.
In a unit cell, atoms or ions can be located at three different positions: within the interior (or bulk), on the face, or on the edge/corner. For simplicity, let's consider a cubic unit cell.
1. Atoms/Ions within the Interior: Each atom/ion located within the interior of the unit cell is completely contained within the unit cell. So, all of its volume is within the unit cell. Therefore, the atoms/ions within the interior contribute the entire volume within the unit cell.
2. Atoms/Ions on the Face: When an atom/ion lies on the face of a unit cell, it is only partially contained within the unit cell. Specifically, half of its volume will be within the unit cell, while the other half will lie outside the unit cell.
Therefore, for each atom or ion on the face of a unit cell, only half of its volume is within the unit cell. Hence, the correct answer is 1/2.