Final answer:
For the angular momentum quantum number l, there are 2l + 1 possible magnetic quantum number value ms and two possible electron spin states. For l=0, 1, 2, 3, you get 1, 3, 5, and 7 orbitals respectively. The minimum principal quantum number n for l=4 is 5 with 9 orbitals.
Step-by-step explanation:
To list the possible ms values for each given angular momentum quantum number (l), we need to understand the relationship between l and ms. The magnetic quantum number, ms, can have values ranging from -l to +l, including zero.
This means for each value of l, there are 2l + 1 possible values of ms. Meanwhile, there are two possible values for the electron spin quantum number ms, which can be either -1/2 or +1/2.
- For l = 0 (s orbitals), the possible ms value is 0. There is only 1 orbital.
- For l = 1 (p orbitals), the possible ms values are -1, 0, +1. There are 3 orbitals.
- For l = 2 (d orbitals), the possible ms values are -2, -1, 0, +1, +2. There are 5 orbitals.
- For l = 3 (f orbitals), the possible ms values are -3, -2, -1, 0, +1, +2, +3. There are 7 orbitals.
The lowest value of the principal quantum number n for which l = 4 can occur is n = 5. This is because l must always be less than n. Therefore, when l = 4, the ms values range from -4 to +4, resulting in 9 possible orbitals.