Answer
There are 18 electron states in the $n=3$ shell.
Work Step by Step
For each $n$, the total number of electron states in the shell is $2n^2$
We can find the number of electron states in the $n=3$ shell:
$2n^2 = (2)(3)^2 = 18$
There are 18 electron states in the $n=3$ shell.