a question on basic quantum mechanics...
when i integrate the square of the wave function (only radial dependence) radially, of this space S, the value obtain should be probabilty per volume right?
so i'll have to multiply this value by some volume
but what?
the size of the atom? or the volume of space S i'm interested?
if it's the size of the atom....then what is it? the size varies on where the electrons are......errr....
confused, please help.

thanks in advance.

a question on basic quantum mechanics...
when i integrate the square of the wave function (only radial dependence) radially, of this space S, the value obtain should be probabilty per volume right?
so i'll have to multiply this value by some volume
but what?
the size of the atom? or the volume of space S i'm interested?
if it's the size of the atom....then what is it? the size varies on where the electrons are......errr....
confused, please help.

thanks in advance.

No, the square of the wave function (or to be more accurate it is the absolute value of the square) is the probability per volume, before the integration (it is a probability density, not a probability). If you have a wave function Ψ (x), then |Ψ (x)|² d³x is the probability to find the particle at the volume d³x centered at x (here x means the location vector). When you integrate you get the probability of finding the particle in the volume of integration.

I see.
Thanks!
this was driving me crazy the entire night. ahh...