# How to get the volume per atom when given the unit cell size?

• rwooduk
In summary: You have two atoms in each cube, and you have the volume of each cube. So, if you divide the volume of each cube by the number of atoms in each cube, you get the volume per atom for each cube. Since all the cubes are identical and there is no space between them, this is also the total volume of all the cubes divided by the total number of atoms in all the cubes.
rwooduk
1. estimate the fermi energy for lithium... the crystal structure of lithium is a bcc with a unit cell size of 3.5*10^-10 m

i need n, which equals N / V. if i divide by per atom, then i get (N/atom) / (V/atom) = valance / (V/atom). my question is how to get the volume per atom?

bcc's have 2 atoms per unit cell.

volume per atom should be ~10^28 , how do i get this from the unit cell size?

Thanks for any help.

also, not given density etc, just given valance and unit cell size.

Well since it's a crystal, the order is long range, so I think you can just divide the amount of atoms in one cell with the volume of the cell to get the answer.

1 person
You're given the length of one side of the cube of the bcc structure. Use geometry to figure out the volume surrounding one atom.

1 person
If s is the length of a side of a cube, what is the equation for the volume of the cube?

Chet

1 person
thanks for the replies!

ok so the volume of the cube is (3.5*10^-10)^3

if i divide this into the number of atoms (2) then i do get an answer of the right magnitude.

however i can't see this visually, how does dividing the volume of the cube into the number of atoms give the volume per atom?

please could someone explain a little further, thanks again.

If you are given the number of atoms(n) and volume of each atom(v) and asked to find the total volume(V) what would you do?

1 person
rwooduk said:
thanks for the replies!

ok so the volume of the cube is (3.5*10^-10)^3

if i divide this into the number of atoms (2) then i do get an answer of the right magnitude.

however i can't see this visually, how does dividing the volume of the cube into the number of atoms give the volume per atom?

please could someone explain a little further, thanks again.
You have two atoms in each cube, and you have the volume of each cube. So, if you divide the volume of each cube by the number of atoms in each cube, you get the volume per atom for each cube. Since all the cubes are identical and there is no space between them, this is also the total volume of all the cubes divided by the total number of atoms in all the cubes.

Chet

1 person
Chestermiller said:
You have two atoms in each cube, and you have the volume of each cube. So, if you divide the volume of each cube by the number of atoms in each cube, you get the volume per atom for each cube. Since all the cubes are identical and there is no space between them, this is also the total volume of all the cubes divided by the total number of atoms in all the cubes.

Chet

ahh of course! i see it now, many thanks!

PhysicoRaj said:
If you are given the number of atoms(n) and volume of each atom(v) and asked to find the total volume(V) what would you do?

yep, got it now, thanks for the reply!

## 1. How do you calculate the volume per atom when given the unit cell size?

To calculate the volume per atom, you first need to determine the volume of the unit cell. This can be done by multiplying the lengths of each side of the unit cell. Next, you need to count the number of atoms in the unit cell. Finally, divide the volume of the unit cell by the number of atoms to get the volume per atom.

## 2. What is the unit of measurement for volume per atom?

The unit of measurement for volume per atom is typically cubic angstroms (Å3). This unit is commonly used in chemistry and materials science to describe the volume of individual atoms.

## 3. Can the volume per atom be negative?

No, the volume per atom cannot be negative. The volume of an atom is a physical quantity that cannot have a negative value. If you get a negative value when calculating the volume per atom, you should double-check your calculations.

## 4. How does the volume per atom affect the density of a material?

The volume per atom is directly related to the density of a material. As the volume per atom decreases, the density of the material increases. This is because the atoms are packed closer together, resulting in a higher mass per unit volume.

## 5. Can the volume per atom be different for different types of atoms in a unit cell?

Yes, the volume per atom can be different for different types of atoms in a unit cell. This is because different types of atoms have different sizes and therefore occupy different volumes within the unit cell. To calculate the overall volume per atom for a unit cell with multiple types of atoms, you would need to take into account the number of each type of atom in the unit cell.

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