Assume that the aluminum atoms can be represented as spheres, as shown in the drawing (Part C figure) . If each atom has a radius of 1.43 , what is the length of a side of the unit cell?
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To find the length of a side of the unit cell, we need to understand the concept of unit cell and its geometry. A unit cell is the basic repeating unit in a crystal lattice. In this case, we are considering aluminum atoms, which are assumed to be arranged in a simple cubic lattice.
A simple cubic lattice consists of atoms arranged in a cube, with each atom at the corner. The length of a side of the unit cell can be determined by considering the distance between adjacent atoms.
In a simple cubic lattice, each atom touches its six neighboring atoms along the edges of the cube. Since each aluminum atom has a radius of 1.43 Å (angstroms), the diameter of each atom is twice the radius, which is 2.86 Å.
The distance between the centers of two adjacent atoms along an edge of the cube is equal to the sum of their radii. Therefore, the distance is 2.86 Å.
Since the length of one side of the unit cell is the distance between two adjacent atoms along an edge of the cube, the length of a side of the unit cell is also 2.86 Å.
In summary, the length of a side of the unit cell in this arrangement is 2.86 Å.