Determine for solid manganese (Mn) the following:

What is the atomic density (atoms/m) along the [110] direction of the Mn crystal?

What are the number of nearest neighbors around an atom in the Mn crystal?

Calculate the interplanar spacing (m) between {220} planes in the Mn crystal.

For molibdenium

We see from the PT that Mo is a BCC material, so the face diagonal [011] has 2⋅(12) atoms over a distance of 2√a.

The value of the lattice parameter a can be found in the same manner as the previous problem (noting that the BCC structure has only 2 atoms per unit cell rather than 4). Thus,

1 atom2√a=12√(2VmolarNAv)1/3=2.24×107

2.44e9

gg is right

To determine the atomic density along the [110] direction of solid manganese (Mn), we need to consider the crystallographic structure of Mn.

1. Atomic Density (atoms/m) along the [110] Direction:
a. Find the lattice parameter (a) of solid Mn. This information can be found in reference materials or databases.
b. Determine the Miller indices for the [110] direction. In this case, [110] represents three planes intersecting at right angles. The Miller indices for the [110] direction are (1, 1, 0).
c. Calculate the length of the [110] direction. The length can be calculated using the formula:
Length = a * sqrt(h^2 + k^2 + l^2)
where h, k, and l are the Miller indices.
d. Determine the number of atoms in a unit cell of Mn. This can also be found in reference materials or databases.
e. Calculate the atomic density using the formula:
Atomic Density = Number of atoms in the unit cell / Length

2. Number of Nearest Neighbors around an Atom:
a. Identify the crystal structure of solid Mn. This information can be found in reference materials or databases.
b. Determine the coordination number, which is the number of nearest neighbors around an atom in the crystal structure. The coordination number depends on the crystal structure of Mn.

3. Interplanar Spacing (m) between {220} planes:
a. Find the lattice parameter (a) of solid Mn. This information can be found in reference materials or databases.
b. Determine the Miller indices for the {220} planes. In this case, {220} represents three planes intersecting at angles. The Miller indices for {220} are (2, 2, 0).
c. Calculate the interplanar spacing using the formula:
Interplanar Spacing = a / sqrt(h^2 + k^2 + l^2)
where h, k, and l are the Miller indices.

Please note that the specific values required for calculations, such as lattice parameters and number of atoms in the unit cell, may vary depending on the specific crystal structure of solid Mn being considered.