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

[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.

 

[kontejnjer]

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.

 

[vela]

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.

 

[Chestermiller]

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

Chet

 

[rwooduk]

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.

 

[PhysicoRaj]

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?

 

[Chestermiller]

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

 

[rwooduk]

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!

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!