N L ML Atoms, Orbitals, number of electrons

[Javier Perez M 1H]

Hi, can someone explain to me what the significance is of each and how to find the number of electrons when Ml is given? Im having trouble understanding what ml means the most when finding the number of electrons.

[Steph Du 1H]

The principal quantum number (n) gives the energy and size of the orbital. It is known as the shell. The angular momentum quantum number (l) gives the shape of the orbital where l=0 is s-orbital, l=1 is p-orbital, l=2 is d-orbital, and l=3 is f-orbital. This is a subshell. The magnetic quantum number specifies the orbital within a subshell which is its different orientations.
For example, given a value of n=2, the possible values of l are l=0 and 1. If we take the value of l=1, the possible values of ml=-1, 0, +1. This denotes the 2px, 2py, and 2pz orbitals because n=2, so the shell is 2, l=1 so the subshell is p, and ml denotes the orientations x, y, and z. The allowed values of l are 0, 1, 2,..., with the greatest number possible being n-1. So for n=2, your highest l value is 1 so your values are 0 and 1. The allowed values of ml are l, l-1,..., -l. Your values must be between l and -l. Thus we have 1, 1 minus 1 which is 0, and -1.

[Emily Vu 1L]

Hi Javier! I think Steph gave a pretty exhaustive explanation so I will try to add onto that/explain it in a different way that helps. So the significance of the quantum numbers (in general) is to locate a particular electron in an atom. What Dr. Lavelle emphasized repeatedly is that the first three quantum numbers (n, l, ml) were what were discovered from Schrodinger's equation and ms (or spin) was determined thereafter. n simply designates the energy level with which an electron resides at a particular time. It is the broadest quantum number to describe an electron's state as for any electron, there is a possibility that the electron can reside within a minimum of one or even up to four subshells within this energy level. These subshells, given by l, are s, p, d, and f. l (angular momentum quantum number) is just a numbering system that designates the s orbital as l=0, p as l=1, d as l=2, and f as l=3. And finally ml describes, within those subshells, the possible states where an electron can be found. So a good way to think about it is that n--> l --> ml locates an electron with increasing specificity.

If ml is given, we know that only up to 2 electrons can exist in that state (for p, this could be the px, py, or pz state). If we take the last quantum number (ms), this value then makes locating an electron's state even more specific by determining which electron out of the two is being located.

[allyssa bradley 1H]

I was also initially confused about this on the homework, and the above explanations are super thorough and helpful, so thanks guys! If you want some review, Lavelle goes over ml in lecture 3.3 right after the electron spin experiment. He posts this formula that was really helpful to me:

ml = l, l-1, … -l

So using the translations of l depending on the letter orbital value (s, p, d, f) reviewed in previous responses, your range for ml would be +/- that l value and every whole number in between, including zero. If your l is 0 (associated with s), then ml is just zero. Hope that helps!