Energy Levels: UNIZOR.COM - Physics4Teens - Atoms - Electronic Structure of Atoms
Channel: Zor Shekhtman on UNIZOR Education
Date: 30/01/2023

UNIZOR.COM - Physics through a Looking Glass of Mathematician
Notes to a video lecture on http://www.unizor.com

Energy Levels

In the previous lecture we have addressed how electrons are positioned around nucleus.
We mentioned that, according to Bohr's model, they are only located on stationary orbits within shells and subshells.

We had a nice formula for the maximum number of electrons that can be located on each subshell, depending on its order number, traditionally designated by a letter (subshell #1 is designated letter s, the next #2 is p, then d, f, g etc.) For subshell #m the maximum number of electrons on it is 4m−2.
The number of subshells within shell #N is N.
Consequently, the maximum number of electrons held in each shell is 2·N².

This mathematically perfect picture gets more complicated, when we consider the energy level associated with each subshell.
The main principle of distribution of energy among subshells, that is, the greater radius of a subshell - the greater energy electrons within this subshell possess, is absolutely true.
The problem is, the further we go from the nucleus - the closer to each other are the shells and, subshells of greater radius of a shell #N might overlap with subshells of smaller radius of shell #N+1.

Let's consider a few elements in a sequence of their atomic numbers, that is the number of protons in their nucleus or electrons within shells on different levels.

Hydrogen has only one proton in the nucleus and one electron within the first subshell (designated by a letter s) of the only shell #1.
So, the electron structure of the atom of hydrogen, where the number specifies the shell number and a letter specifies the subshell, where the superscript at the subshell letter indicates the number of electrons within the same subshell, is:
1s1

Helium has two protons in the nucleus and two electrons within the first subshell (designated by a letter s) of the only shell #1.
The subshell s (the first one) can hold maximum of 2 electrons, so everything is fine.
The electron structure of the atom of helium is:
1s2

Lithium has three protons in the nucleus and three electrons.
The first (and only) subshell s of the shell #1 can hold only 2 electrons. Therefore, a new shell #2 should exist and one electron should be in its first subshell s.
The subshell s of the second shell can hold maximum of 2 electrons, so everything is fine.
The electron structure of the atom of lithium is:
1s2 2s1
[Full description is on UNIZOR.COM - Physics 4 Teens - Atoms - Electronic Structure of Atoms - Energy Levels]