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The azimuthal, or angular momentum, quantum number, l, defines the type or shape of the orbital where the electron most probably resides. It is the second ...
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Quantum numbers work like addresses for electrons in an atom. To narrow down your intended recipient, you would write the state city street street number to tell the post office where to go. Quantum numbers work the same way: energy level type of orbital orientation of orbital orientation of electron. Every electron in an atom will have a unique set of quantum numbers in the form [n, l, m l, ms].
The principal quantum number, n , defines the energy level or shell of the electron. It is the first quantum number that must be determined, as it defines the available values for all other quantum numbers. Think of Bohr’s model for the atom; n defines the ring on which the electron resides.
The value of n tells you how many levels away from the nucleus the electron is. The valence shell of an atom is the highest occupied shell and is mathematically equivalent to the period of the element (i.e., H is in period 1, so the valence shell for H is n = 1).
The azimuthal, or angular momentum, quantum number, l , defines the type or shape of the orbital where the electron most probably resides. It is the second quantum number to be determined as its value relies only on n (i.e., if n = 2, then l = 0 or 1 since n – 1 = 1). Each type of orbital has a unique number of nodes (e.g., where the wave changes phases) which is mathematically equivalent to l. If l = 0, the electron is in an s-orbital that has 0 nodes. If l = 1, the electron is in a p-orbital that has 1 node. If l = 2, the electron is in a d-orbital that has 2 nodes. If l = 3, the electron is in an f-orbital that has 3 nodes.
s-orbital p-orbital d-orbital f-orbital
The magnetic quantum number, ml, defines the orientation of the orbital in which the electron
inhabits. The number of ml values is called the degeneracy, or the number of orbitals in the
atom that are at the same energy level. Note that to have the same energy, the orbitals must be on the same energy level as well as be the same type of orbital ( n and l values are equal). A
2s orbital is not degenerate (e.g., the same energy) with a 2p or a 1s orbital.
The ml values are entirely dependent on the l values; each type of orbital has a set degeneracy.
For an s-orbital, ml = 0, and degeneracy = 1. For a p-orbital, ml = -1, 0, +1, and degeneracy = 3. For a d-orbital, ml = -2, -1, 0, +1, +2, and degeneracy = 5. For an f-orbital, ml = -3, -2, -1, 0, +1, +2, +3, and degeneracy = 7.
NOTE: A set of 2p orbitals and 3p orbitals may have the same degeneracy value , but they are NOT degenerate with each other. They both include three total orbitals, but they are not at the same energy: they have different n values.
The spin quantum number, ms, is completely independent of the values of n, l, and ml. It is always
As of yet, we cannot determine whether an electron is pointed up or down, so it can be assumed always that ms = ± ½