Lattice constant and volume density

[orangeincup]

Homework Statement

a) A material is composed of two atoms, A with effecitve radius 2.00 angstroms and B with effective radius 3.10 angstroms. The lattice is a body-centred lattice.
b)Enter the volume density of either the A or B atoms in atoms/cm3

Homework Equations

.5*sqrt3=(r1+r2)
surface density=# of atoms per lattice plane/area of lattice plane

The Attempt at a Solution

a)
a=((3.10A+2.0A)*2)/(sqrt3)
a=5.89 A (Lattice constant) (correct)

b) In part B I keep getting the wrong answer.

The equation I'm using is surface density=# of atoms/area of lattice plane

So...
# of atoms should be 2 for a body centered cube
2/(5.89*10^-8)^3 = 9.79*10^21 atoms/cm^2 (incorrect)

 

[mfb]

As far as I remember, body-centered here refers to the symmetry alone: the central atom has the same type as the corners, the other atoms are in between.

As an example, Caesium chloride would fit your calculation, but its crystal structure is simple cubic.

But then I'm surprised that the lattice constant is right.

Do you mix surface and volume density here?