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### Z^2 in Schrodinger Equation

Posted: Sun Oct 20, 2019 5:52 pm
I'm confused by the books definition of trying to explain why Z^2 is more important than Z. The textbook says, "A skill to develop is to think about why a property depends on various parameters in a particular way. In this case you might wonder why the energy depends on Z 2 rather than on Z itself. The reason can be traced to two cooperating factors. First, a nucleus of atomic number Z and charge Ze gives rise to a field that is Z times stronger than that of a single proton. Second, the electron is drawn in by the higher charge and is Z times closer to the nucleus than it is in hydrogen. The two factors work together to give an overall energy lowering that is proportional to Z2." I don't understand the Z and Ze part of the first reason, and why the electron is Z times closer to the nucleus than if it were in a hydrogen.

### Re: Z^2 in Schrodinger Equation

Posted: Sun Oct 20, 2019 10:56 pm
Z is the measure of the number of protons right? The radius of a helium atom is smaller than that of a hydrogen atom because there is a greater positive charge pulling the electrons tighter. Maybe that's what the book is trying to get at?

### Re: Z^2 in Schrodinger Equation

Posted: Sun Oct 20, 2019 11:04 pm
I believe what it is trying to say is that the strength of the nucleus pulling in the electrons is Z^2, which means that as the atomic number number increases, the nuclear charge Ze increases by the factor of Z^2.