Final answer:
For n = 2, there are two possible subshells: 2s and 2p. The 2s subshell with l = 0 can have one ml value of 0, supporting 2 electrons. The 2p subshell with l = 1 has three ml values: -1, 0, 1, each supporting 2 electrons, totaling 6 electrons, and thus 8 electrons can be in the n = 2 shell overall.
Step-by-step explanation:
Possible Subshells and Magnetic Quantum Numbers for n = 2
When the principal quantum number n is equal to 2, there are two possible subshells: the 2s subshell and the 2p subshell. These correspond to the angular momentum quantum number l, which can be 0 for the s subshell and 1 for the p subshell. For the 2s subshell (where l = 0), the magnetic quantum number ml can only be 0. In the 2p subshell (where l = 1), ml can have values of -1, 0, or 1. Therefore, we have the following sets of quantum numbers possible for n = 2:
- 2s subshell: (n=2, l=0, ml=0) with 2 possible electrons due to two spin states ms = +1/2 and ms = -1/2.
- 2p subshell: (n=2, l=1, ml=-1), (n=2, l=1, ml=0), and (n=2, l=1, ml=1), with each ml state having 2 possible electrons due to two spin states.
Therefore, the 2s subshell can hold a maximum of 2 electrons and the 2p subshell can hold a maximum of 6 electrons (2 for each ml value), giving a total of 8 electrons for the entire n = 2 shell.