Question

1. For n = 5, l = 4, what are the possible values of and ml and ms?

2.  Calculate the magnitude of the angular momentum of an electron in the n = 7, l= 5 state of hydrogen.

Answer 1

If n is your principle quantum number, then your angular momentum quantum number, l, is l=0,1,2,.....n-1, your z-component angular momentum ml, is ml=0, +/- 1, +/- 2,+/- 3,......+/- l, and your electrom spin ms, is ms= +1/2 / -1/2.

So if n=5, then l = 0,1, 2, 3 & 4
For l=0, ml=0
For l=1, ml= -1, 0, +1
For l=2, ml = -2, -1, 0, +1, +2
For l=3, ml = -3, -2, -1, 0, +1, +2, +3
For l=4, ml = -4, -3, -2, -1, 0, +1, +2, +3, +4


Ms can be +1/2 or -1/2 for any electron.

n describes the shell of an atom.
l describes the subshell of an atom, l=0 is subshell s, l=1 is subshell p, l=2 is subshell d, l=3 is subshell f and l=4 is subshell g.
ml describes orbitals, for an s subshell (l=1) ml = 0 representing the single orbital in the s subshell, for a p subshell ml= -1, 0, +1 representing the 3 orbitals in the p sunshell, and for a d subshell ml = -2, -1, 0, +1, +2 representing te 5 orbitals in the d subshell etc.

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