Calculate planer density of 110 plane in FCC?

Answer 1

Planar density, atoms per area
To do this you should draw the plane an FCC would make from (1, 1, 0) in a 111 cube.

When you draw this you will see that for the FCC structure, that each of the corners of your rectangular plane has 1/4 of an atom and the diagonal section of the plane has 1/2 of an atom on it (this would be the face atom).

Total atoms = 4*1/4+2*1/2= 2 atoms

the area of this rectangle is base times height
a = edge length of the unit cell

height = a
base = a*sqrt(2)

Area = a^2*sqrt(2)

So the planar density would be

2 atoms/(a^2*sqrt(2))
and if your want to be extra anal it will simplify to
sqrt(2)/(a^2)