Z^2 in Schrodinger Equation



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Bryce Ramirez 1J
Posts: 84
Joined: Sat Aug 24, 2019 12:16 am

Z^2 in Schrodinger Equation

Postby Bryce Ramirez 1J » 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.

Daniel Yu 1E
Posts: 76
Joined: Sat Aug 24, 2019 12:15 am

Re: Z^2 in Schrodinger Equation

Postby Daniel Yu 1E » 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?

Siya Shah 1J
Posts: 50
Joined: Sat Aug 17, 2019 12:15 am

Re: Z^2 in Schrodinger Equation

Postby Siya Shah 1J » 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.


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