posted by charlie .
If energy is 1/2 mv^2; and m and v are always positive....
How come the ground state energy of Hydrogen is a minus value?
The ground state energy of hydrogen is a sum of kinetic and potential energies. The potential energy is DEFINED to be zero when the electron and proton are infinitely far apart. As the electron gets closer, the attractive force between electron and proton makes the potential energy increasingly negative. The absolue value of the negative potential energy exceeds value of the kinetic energy (which is always positive), so the sum of the two energies is always negative.