Quantum Numbers n, l, and m

[Sydney Wu 2M]

I am very confused on the concept on n, l, and m_l...

1) Can the relationship between n, l, and m be described as shell, sub-shell, and orbital within a sub-shell, respectively?
2) Does the l-value tell you the highest possible sub-shell of that particular energy level? (i.e. n=3; l=0, 1, & 2 --> level 3 has 3 sub-shells s, p, & d)
3) What exactly is m_l? (i.e. Q 2.17; how can you calculate the number of orbitals? If l=2, m_l=2-1=1, so doesn't that mean there's is only 1 orbital?)

[cara_Budzinski_3D]

Okay so to answer your questions...
1) yes; if you look in the course reader, that is exactly how they are labelled
2) if i understand your question, then yes; l assigns a value (referred to as subshell) to each orbital (s, p, d, or f) and the highest l value, say l=4, will contain not only the f-orbital but also all orbitals below it as well
3) m(sub l) labels the different orbitals of a subshell, such as p(sub x), p(sub y), & p(sub z); it also represents the spin on the electron which is easier to see when you draw out the electron configuration with the up & down arrows

[Chem_Mod]

Okay so to answer your questions...
1) yes; if you look in the course reader, that is exactly how they are labelled
2) if i understand your question, then yes; l assigns a value (referred to as subshell) to each orbital (s, p, d, or f) and the highest l value, say l=4, will contain not only the f-orbital but also all orbitals below it as well
3) m(sub l) labels the different orbitals of a subshell, such as p(sub x), p(sub y), & p(sub z); it also represents the spin on the electron which is easier to see when you draw out the electron configuration with the up & down arrows

It doesn't also represent the spin... spin has it's own quantum number.