## Problem 6.66

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

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

If you have any questions or comments, reply to chapman@sou.edu

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Doug Chapman chapman@sou.edu 7/15/14