Quantum numbers are like parts of an address. Each one describes some property of the electron, just like how each part of an address gives some information about where a person lives.
ms describes the spin of an electron ms describes the direction in which the electron itself is rotating.
ms describes the spin of the electron itself. ms can have a value of +1/2 (spin up) or -1/2 (spin down)
The Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four electronic quantum numbers. As an orbital can contain a maximum of only two electrons, the two electrons must have opposing spins. This means if one electron is assigned as a spin up (+1/2) electron, the other electron must be spin-down (-1/2) electron. Electrons in the same orbital have the same first three quantum numbers, e.g., n=1, l=0, ml=0 for the 1s subshell. Only two electrons can have these numbers, so that their spin moments must be either ms=−1/2 or ms=+1/2. If the 1s orbital contains only one electron, we have one ms value and the electron configuration is written as 1s1 (corresponding to hydrogen). If it is fully occupied, we have two ms values, and the electron configuration is 1s2 (corresponding to helium). Visually these two cases can be represented as
The 2nd case is correct because the difference of spins in the 2s orbital mean that the electrons do not share all 4 quantum numbers, satisfying the Pauli Exclusion Principle. In effect, the above example shows that for each n shell, l shape, and ml orientation (in the picture each box), there can be a maximum of 2 electrons and if there are 2, they must have opposite spins.
It may seem strange that two electrons could reside in the same slot of an orbital, since electrons all have - charge and like charges repel. However, the property of spin explains this since spin-up and spin-down cause the electron to be slightly more negative/positive. The spins make the charges farther apart and thus they repel each other less, allowing two otherwise identical electrons to reside in the same orbital.
Hund's Rule states that when filling in electrons for a given orbital, they all fill one way first fully and then the other way with regards to spin. This means for an p orbital with 6 slots for electrons, the first 3 fill spin-up, and then the next 3 fill spin down. This important rule can be used to calculate magnetism, unpaired electrons, and more.
With Hund's Rule and the ideas from electron configuration, orbital diagrams can be created. This is shown in the video below:
1) How many unpaired electrons does Cu have?
Answer: 1 (All electrons are paired until the 3d orbital, where filling all spin-up and then all spin-down, we can see there is 1 unpaired spin-up electron)
2) How many possible values of ms are there for n = 5?Answer: 2 ( The values are always +1/2 or -1/2 (spin up or spin down) )