PV = nRT but P = 10

Volume of the atmosphere = 4/3πR

R = 6.4x10

r = 6.40x10

So volume of the Earth's atmosphere = 4/3π(2.63116x10

However the density of this "uniform atmosphere" = 1.293 kgm

Mass of Earth's atmosphere = density x volume = 1.293 x 4.07x10

The mass of a "molecule of air" is about 10

Now using PV = nRT Pressure (P) = 8.73x10

Which is of the right order for the accepted value for the pressure of the atmosphere.

The Earth only has an atmosphere because of the
gravitational attraction of the Earth's field. Without that the molecules would simply disperse
into space. The escape velocity for a given planet is [2Rg]^{1/2} where R is the radius of the
planet and g the gravitational field strength at its surface. So you see that if g = 0 the escape
velocity would also be zero and the planet would lose its atmosphere.