[ILoveISO]

Which are the following sets of quantum numbers are not allowed for an orbital?

1. n=4 l=3 ml= 4 <--- why doesn't this one work

Answer says because of this

ml = 2l+1 -->      2(3)+1 = 7 so ml has to be -3, -2, -1, 0, +1, +2, +3

if that is the case how come this set of quantum number work

2. n=8 l=7 and ml= -6

[Yggdrasil]

For l = 7, the allowed values of m_l range from -7 to 7.  In general, m_l ranges from -l to l.

[ILoveISO]

Yeah but how does that make ml = -6? If it ranges from -7 - 7 wouldn't that be -7, -6, -5, -4, -3, -2, -1 0 1 2 3 4 5 6 7 ?

[Yggdrasil]

-6 is among the allowed values of m_l.  2 would also work, or -5 or 4, or 0, etc.  However, any value outside of that range would not work.

[Borek]

Yeah but how does that make ml = -6?

It doesn't "make" it. It just allows ml=-6.

If it ranges from -7 - 7 wouldn't that be -7, -6, -5, -4, -3, -2, -1 0 1 2 3 4 5 6 7 ?

Any of these will do. It just means that it is possible that for n=8 & l=7 there can exist electron with ml = -6. There can exist also electron with ml=3 or ml=0, or even ml=7, but not one with ml = 11. It dosn't mean that such electron DOES exist, it will exist (in the ground state) only in elements that have enough electrons to fill orbitals up to this one.