how high would the atmosphere extend if it were of uniform density throughout, equal to half the present density at sea level?

Answer 1

Let H be that height.

Solve this equation for h

Po = (1/2)(rho0) g H

Po = 1.01*10^5 N/m^2
(rho0) = sea level average density of air = (approx) 1.2*10^3 kg/m^3
g = 9.8 m/s^2

http://en.wikipedia.org/wiki/Atmospheric_pressure