Answer
$1.2\times10^9~atoms/m^2$
Work Step by Step
First let's calculate the surface area of the earth.
$Area = 4\pi R^2 = 4\pi (6.4\times 10^6 ~m)^2 = 5.1\times10^{14}~m^2$
Now, we find the number of atoms per unit area:
$\frac{6.02\times10^{23}~atoms}{5.1\times10^{14}~m^2} = 1.2\times10^9~atoms/m^2$
