Sodium has bcc packing. If a distance between two nearest atoms is 3.7 A* then what is the lattice parameter?
To find the lattice parameter in a body-centered cubic (bcc) lattice, we need to apply some geometry and mathematical calculations.
In a bcc crystal structure, the atoms are arranged in a cube shape, with one atom at each of the eight corners and an additional atom positioned at the center of the cube. The distance between two nearest atoms (also known as the nearest neighbor distance) can be related to the lattice parameter.
The nearest neighbor distance (d) can be expressed in terms of the lattice parameter (a) using the equation:
d = (√3/4) * a
Rearranging the equation to solve for the lattice parameter (a), we have:
a = (4/√3) * d
Now we can substitute the given nearest neighbor distance (d = 3.7 Å) into the equation:
a = (4/√3) * 3.7 Å
Calculating this expression, we get:
a ≈ 5.640 Å
Therefore, the lattice parameter for sodium in a bcc structure is approximately 5.640 Å.