Example 30.4 from College Physics, 30.9 The Pauli Exclusion Principle

How Many Electrons Can Be in This Shell?

List all the possible sets of quantum numbers for the $n = 2$ shell, and determine the number of electrons that can be in the shell and each of its subshells.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Given $n = 2$ for the shell, the rules for quantum numbers limit $l$ to be 0 or 1. The shell therefore has two subshells, labeled $2 s$ and $2 p$ . Since the lowest $l$ subshell fills first, we start with the $2 s$ subshell possibilities and then proceed with the $2 p$ subshell.
Solution
It is convenient to list the possible quantum numbers in a table, as shown below.

Figure 30.60
Discussion
It is laborious to make a table like this every time we want to know how many electrons can be in a shell or subshell. There exist general rules that are easy to apply, as we shall now see.

0 of 3 steps open

How did it go?

Strategy

Solution

Discussion

Strategy

Solution

Discussion