## Degeneracy

Ramsha Dis1B
Posts: 32
Joined: Fri Sep 28, 2018 12:19 am

### Degeneracy

I don't understand what degeneracy means and how we determine the degeneracy of a certain orbital, like 3p. How would you determine that?

Andie Jian 1D
Posts: 69
Joined: Fri Sep 28, 2018 12:17 am
Been upvoted: 1 time

### Re: Degeneracy

Degeneracy means the same energy. For example, with hydrogen, every subshell in the same energy level will be degenerate, because there is no electron-electron repulsion countering the pull of the nucleus, as there is only one electron. However, with multi-electron atoms, the subshells within the same energy level become degenerate, having different energy levels in the order of s<p<d<f. Subshells of lower energy are able to "shield" or offset the pull of the nucleus for subshells of higher energy (within the same shell). The reason these subshells have differing energies depends on how well they are able to penetrate the nucleus. The s subshell has no nodes, meaning it has a non-zero probability of being found in the nucleus. Therefore, it is able to penetrate the nucleus unlike the other subshells, therefore more effectively shielding the other electrons. However, with each increasing subshell type, there is more and more angular momentum driving the electron away if it gets to the nucleus, so they are less and less able to get close to the nucleus, staying at further at a higher energy level instead.

Julia Lee
Posts: 80
Joined: Fri Sep 28, 2018 12:29 am

### Re: Degeneracy

Im pretty sure that the degeneracy of a 3p orbital would just be 3 since 3px, 3py, and 3pz all have the same energy level in a multi-electron atom.

Ramsha Dis1B
Posts: 32
Joined: Fri Sep 28, 2018 12:19 am

### Re: Degeneracy

Oh okay, so if is asking the degeneracy for 3s it would be 3 too? And if it was asking for 4p it would be 4?

Chloe Orsini 1K
Posts: 32
Joined: Fri Sep 28, 2018 12:18 am

### Re: Degeneracy

I looked this up to try to help and online all it said was to square the value of n, so if n=3 than the degeneracy is 9, is this correct?

George Ghaly 2L
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Joined: Fri Sep 28, 2018 12:29 am
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### Re: Degeneracy

As far as degeneracy is concerned it is important to know that electrons in the same hydrogen atom have the same energy level. However, multi electron systems are not degenerate as with different sub shells there are different energies.

Sana_Mian_3G
Posts: 30
Joined: Fri Sep 28, 2018 12:23 am

### Re: Degeneracy

I know that n equals the energy level. So would that mean if they have the same energy level would it just be n=3 or 3s, 3p, and 3d?

Danny Zhang 4L
Posts: 62
Joined: Fri Sep 28, 2018 12:26 am

### Re: Degeneracy

For hydrogen, all orbitals share the same energy, so the degeneracy of an orbital simply depends on how many exist. For multi-electron atoms, only orbitals that share the same l quantum number have the same energy, so the degeneracy of an orbital would then depend on how many possible orbitals is possible for the indicated l quantum number.