maximum number of electrons - quantum numbers

Question

In an atom, what is the maximum number of electrons that can have the following quantum numbers?

(a) n = 4, ms = -1/2



(b) n = 7, l = 4


(c) n = 4, l = 1, ml = +1


(d) n = 5, l = 2, ml = +1

Answer 1

(a) n = 4, ms = -1/2
Number of electrons is 2n², where n is the quantum number. So for n=4, total electrons = 2x4² = 32.  One half of them can have ms=-1/2. So there can be 16 electrons with n=4, ms=-1/2.

(b) n = 7, l = 4

When l = 4, this tells you it is a 'g sub shell'.  Thus, there will be a total of 18 electrons.

(c) n = 4, l = 1, ml = +1

When l = 1, this tells you it is a 'p sub shell', and ml can be -1, 0, or +1.  Here it is +1.  When l=+1, you can have ms = +1/2 or -1/2, so there could be 2 electrons with such quantum numbers.


(d) n = 5, l = 2, ml = +1

This is similar to (c) above.  Since ml = +1, this limits the number of electrons to 2 since everything else is fixed, and you are looking only at ml = +1 and not the others (-2,-1,0, +2)