Question

What is the maximum number of electron in an atom that can have the following quantum numbers? (a) n = 3, ml = -2; (b) n = 4, l = 3; (c) n = 5, l = 3, ml = 2; (d) n = 4, l = 1, ml = 0.

Answer 1

(a) n = 3, ml = -2;

if mL = -2; then, we can choose from:

l = n-1 = 3-1 = 2

so this is the max mL value and only one we can have

so

+/- 1/2 spins, total of 2 electrons

(b) n = 4, l = 3;

we could have:

ml = 0, +/-1, +/-2, +/-3,

each will have +/- spins, so

totla ml = 1,2,2,2 = 7

times two spins

7*2 = 14 electrons

(c) n = 5, l = 3, ml = 2;

for ml = 2, we could only have +/- 1/2 spins --> 2 electrons

so total of 2 electrons

(d) n = 4, l = 1, ml = 0.

once again, we could only have +/- 1/2 spins --> 2 electrons