Ground State Energies of He+ Ion

[joker314]

Homework Statement

What are the energies of the ground state and the first two excited states of the He⁺ ion?

Homework Equations

E_n= - E_o/n²

The Attempt at a Solution

n=1 for this problem (since there is only 1 electron) so the ground state would have the electron contained in the 1s subshell. Thus E= -13.6eV(1/1²)=-13.6eV

The first excited state has the electron entering the 2s subshell, and the second excited state in the 2p subshell? What I'm getting confused about (assuming my solution for E for the ground state is correct) is that since n=1, the answer won't change depending on what subshell it is in according to how I am approaching the problem. And this I believe is incorrect... Any thoughts, help? Thanks!

 

[Dick]

Ok. Doesn't the energy of the ground state of a one electron atom depend on the charge of the nucleus? -13.6eV is the ground state energy for hydrogen. The general formula depends on Z^2 where Z is the charge of the nucleus. Look it up!

 

[joker314]

Ok I see where the textbook was getting the -13.6 eV from now, I was looking at the section on the Hydrogen atom since I knew I needed to be dealing with one electron atoms. According to the textbook it is -78.98 eV. So then is the energy in the two excited states goin to be this value squared?

 

[Dick]

The two excited states are n=2 and n=3 for Z=2 nucleus. There is also a 1/n^2 in the formula you are looking for.

 

[joker314]

I understand now how to find the energies of the first two excited states by using the ground state energy. I do not however understand how to get the ground state energy without looking it up. What formula would I use?

 

[Dick]

I understand now how to find the energies of the first two excited states by using the ground state energy. I do not however understand how to get the ground state energy without looking it up. What formula would I use?

http://en.wikipedia.org/wiki/Hydrogen-like_atom Skip down to the formula for E_n. The ground state is the energy for hydrogen times Z^2.