Answer
The thickness of the atmosphere would be 7.95 km
Work Step by Step
The atmospheric pressure at the earth's surface would be equal to $\rho~g~h$, where $h$ is the total thickness of the atmosphere. Therefore;
$\rho~g~h = P_0$
$h = \frac{P_0}{\rho~g}$
$h = \frac{1.013\times 10^5~N/m^2}{(1.3~kg/m^3)(9.80~m/s^2)}$
$h = 7950~m = 7.95~km$
The thickness of the atmosphere would be 7.95 km
