## Problem 6.66

### What is the maximum number of electrons in an atom that can have the following quantum numbers?

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

When n=2, we can have l=0,1; thus we have the 2s and 2p subshells. The 2s subshell contains one orbital (ml = 0); this orbital can hold two electrons, one of which has spin quantum number=-1/2. The 2p subshell contains three orbitals (ml=-1, 0, 1); each orbital can hold two electrons, and the 2p subshell can hold 6 electrons. Three of these electrons can have m2 = -1/2, so a total of 4 electrons can have n=2, ms =-1/2.

(b)n=5, l=3

Here, we get a little more specific; we specify the n and l quantum numbers. This is the 5f subshell; since l=3, ml = -3,-2, -1, 0, 1, 2, 3. Thus, we have 7 orbitals, each of which can hold two electrons, giving a total of 14 electrons which can have n=5, l=3.

(c)n=4, l=3, ml=-3

When we specify three quantum numbers, we are specifying an orbital; thus, only two electrons in an atom may have these three quantum numbers (and their spin quantum numbers must be different).

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

These three quantum numbers represent an orbital in the 4s subshell; two electrons may have these quantum numbers (meaning that they reside in the same orbital), but thier spin quantum numbers must be different.