- #1

- 331

- 0

Are there any equations the show why this occurs?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter nuby
- Start date

- #1

- 331

- 0

Are there any equations the show why this occurs?

- #2

G01

Homework Helper

Gold Member

- 2,682

- 17

It is due, first due to the degeneracy of the energy shell (i.e. how many energy states that have that shell's energy) and also due to the pauli exclusion principle.

First, the higher energy shells have bigger degeneracies. In simple terms, there are more orbitals in the n=2 shell than there are in the n=1 energy shell. Thus, they can hold more electrons. Each orbital can hold a maximum of two electrons with opposite spin due to the Pauli principle. So the end result is:

n=1 Shell: 1 orbital = 2 electrons

n=2 Shell: 4 orbitals= 8 electrons

n=3 Shell: 9 orbitals= 18 electrons

The number of orbitals is determined by the number of possible angular momentum states for the electrons in the atom, which is predicted by the Schrödinger Equation. So, while your pattern may seem nicer or more aesthetic, it is not what the Schrödinger Equation predicts, so it does not make more sense mathematically in the end.

First, the higher energy shells have bigger degeneracies. In simple terms, there are more orbitals in the n=2 shell than there are in the n=1 energy shell. Thus, they can hold more electrons. Each orbital can hold a maximum of two electrons with opposite spin due to the Pauli principle. So the end result is:

n=1 Shell: 1 orbital = 2 electrons

n=2 Shell: 4 orbitals= 8 electrons

n=3 Shell: 9 orbitals= 18 electrons

The number of orbitals is determined by the number of possible angular momentum states for the electrons in the atom, which is predicted by the Schrödinger Equation. So, while your pattern may seem nicer or more aesthetic, it is not what the Schrödinger Equation predicts, so it does not make more sense mathematically in the end.

Last edited:

- #3

- 331

- 0

Is this possible? n=6

71.5 electrons?

71.5 electrons?

- #4

Danger

Gold Member

- 9,647

- 252

Is this possible? n=6

71.5 electrons?

That might be a bit difficult; splitting an electron in half is not something that you just do with a hammer and chisel...

- #5

- 331

- 0

Lol. nevermind

Last edited:

- #6

- 2,268

- 7

dont forget that the nucleus also has shells and subshells.

Share: