Identify each of the four quantum numbers and the properties to which they refer.?

Answer 1

For atomic electrons,

The principal quantum number, n, is related to the eigenvalues of the Hamiltonian (or "total energy" if you don't speak Quantum).

The orbital quantum number, l, is related to the orbital angular momentum of the electron. It ranges from 0 to n - 1 by integers. For example, if n = 3, l can be 0, 1, or 2.

The magnetic quantum number, m, is related to the projection of the orbital quantum number onto a specific axis. The values range from -l to +l and differ by exactly 1. For example, if l = 2, m can be -2, -1, 0, +1, or +2.

The spin quantum number, s, is the projection of the spin onto a specific axis. The values can be +1/2 and -1/2 (commonly called "up" and "down")

Answer 2

n = principle quantum number => energy level
l = azimuthal quantum number => angular momentum
m = magnetic quantum number => available energy levels within a shell
s = spin quantum number => I think it shows which direction the angular momentum is pointing (electrons are point particles and don't actually spin, but they do have angular momentum as if they were)

For Hydrogen:
n is an integer greater than or equal to 1.
l is an integer between 0 and n-1 (inclusive)
m is an integer between -l and +l (inclusive)
s is + 1/2 or - 1/2 (for electrons/neutrons/protons).

Answer 3

magnetic quantum number( ML) It describe the direction of an atomic orbital. Also shows the number of orbitals in a subshell.The allowed values are ml=-l,0+1, ml=2l+1.