alt.sci.physics

Hello,
Today I was studying our 1st chapter of nuclear physics, (Giancoli) and it
dealt with binding energy.
Since it costs energy to split an alfa particle up into 2 protons and 2
neutrons, the mass of the alfa particle is less than the sum of the mass of
2p & 2n.
Now, to my surprise it was also mentioned in the book that when you bring an
electron infinitely away from a H-nucleus, the total MASS of the system has
been risen with 13,6 eV.

My question is: isn't this energy-increment been counted double??
Since: I would expect that if I put 'effort' in an electron to get it away
from a H-nucleus, either the energy has been converted into *potential*
energy, OR in a mass-increase.
But as I understand the story now, the potential energy of the electron
increases AS WELL AS the mass.
Or is the *mass*change more something like an 'indicator' for
potential-energy change, rather than an energy-carrier?

And if so: does it work the same with gravitational energy?
. when I walk up the stairs, does my energy increase as
well as the mass of the earth-person system?

I just try to get the concept here. who can help me a bit?
;-)

kind regards,
martin