Which of the following combinations of quantum numbers (n, l, ml, ms) do not represent permissible solutions of the schrodinger equation for the electron in the hydrogen atom?
a) 9, 7, -4, 1/2
b) 8,2, 2, 1/2
c) 6, -5, -1, 1/2
d) 6, 5,-5, 1/2
e) all of the above

i'd like to know how to do this please :D

Question

Which of the following combinations of quantum numbers (n, l, ml, ms) do not represent permissible solutions of the schrodinger equation for the electron in the hydrogen atom?
a) 9, 7, -4, 1/2
b) 8,2, 2, 1/2
c) 6, -5, -1, 1/2
d) 6, 5,-5, 1/2
e) all of the above

i'd like to know how to do this please :D

anonymous · Answer

Each quantum number has restrictions:

(1) n must be an integer between 1 and infinity.

(2) l must be an integer between 0 and n-1.

(3) m_l must be an integer between -l and +l, including 0.

(4) m_s must be +1/2 or -1/2.

So, looking at your list, (c) violates Rule 2, but all of the others look OK to me.

lgbasallote · Answer

@carl_pham these 4 restrictions are the permissible solutions of the schrodinger equation?

anonymous · Answer

Sort of.  If you're thinking the SE has many "impermissible" solutions, e.g. {2,3,2,-1/2}, and you can't use these for some reason, that is not correct.  Rather, it's that every solution of the SE is described by a set of four quantum numbers which follow the rules above.  Any set of four numbers that does NOT follow these rules does NOT describe a solution of the SE.