Density and Lattice Type of Lithium Metal

Lithium Metal Density
The given density of Lithium metal is 0.53 gm/m^3. Density is defined as the mass per unit volume of a substance. In this case, it tells us how much mass of Lithium is present in one cubic meter of space.

Lattice
The structure of a solid material can be described in terms of its lattice, which is a repeating pattern of atoms. Lithium metal forms a crystalline lattice structure, where each lithium atom is surrounded by other lithium atoms in a regular arrangement.

Interplanar Spacing
The separation of the (100) planes of the Lithium metal lattice is given as 350 pm. Interplanar spacing refers to the distance between adjacent planes of atoms in a crystal lattice. In this case, the distance between the (100) planes is 350 pm (picometers), which is a measure of length.

FCC and BCC Lattice Types
There are two common types of lattice structures: face-centered cubic (FCC) and body-centered cubic (BCC). In an FCC lattice, each corner of the unit cell is shared by four neighboring unit cells, and there is an additional atom at the center of each face. In a BCC lattice, each corner of the unit cell is shared by eight neighboring unit cells, and there is an additional atom at the center of the unit cell.

Determining the Lattice Type
To determine whether the lattice of Lithium metal is FCC or BCC, we can calculate the theoretical density of Lithium based on the assumption of each lattice type and compare it with the given density.

Calculating Theoretical Density for FCC Lattice
For an FCC lattice, the theoretical density can be calculated using the formula:
Density = (Number of atoms per unit cell) * (Atomic weight of Lithium) / (Volume of unit cell)
The number of atoms per unit cell in an FCC lattice is 4, since each corner atom is shared by 8 unit cells and each face atom is shared by 2 unit cells. The atomic weight of Lithium is 6.94 g/mol.

Calculating Theoretical Density for BCC Lattice
For a BCC lattice, the theoretical density can be calculated using the same formula as for FCC lattice. The only difference is the number of atoms per unit cell, which is 2 for a BCC lattice since each corner atom is shared by 8 unit cells and there is an additional atom at the center of the unit cell.

Comparing Theoretical and Given Density
By comparing the theoretical densities calculated for both FCC and BCC lattices with the given density of Lithium metal, we can determine which lattice type is more likely.

Conclusion
Based on the comparison between the theoretical densities, we can conclude whether the lattice of Lithium metal is FCC or BCC.