Final answer:
The n=3 shell has possible quantum numbers for the s, p, and d subshells, with a total capacity of 18 electrons: 2 in 3s, 6 in 3p, and 10 in 3d.
Step-by-step explanation:
To determine the possible sets of quantum numbers for the n=3 shell and the number of electrons that can be in the shell and its subshells, we follow certain rules derived from quantum mechanics.
The principal quantum number n defines the shell, with n=3 indicating the third shell.
The azimuthal quantum number l can have integer values from 0 to (n-1), so for n=3, l can be 0, 1, or 2. These correspond to the subshells labeled s, p, and d, respectively.
The magnetic quantum number ml ranges from -l to +l, so for each value of l:
For l=0 (the 3s subshell), ml can only be 0.
For l=1 (the 3p subshell), ml can be -1, 0, or 1.
For l=2 (the 3d subshell), ml can be -2, -1, 0, 1, or 2.
The spin quantum number ms can be +1/2 or -1/2 for any electron.
Using the formula 'maximum number of electrons that can be in a subshell = 2(2l + 1)' we find:
For the 3s subshell (l=0), there is space for 2 electrons.
For the 3p subshell (l=1), there are spaces for 6 electrons.
For the 3d subshell (l=2), there are spaces for 10 electrons.
The total number of electrons that can be in the n=3 shell is the sum of electrons in each subshell, which amounts to 2 + 6 + 10 = 18 electrons.