Maximum number of electrons in n=4 l=3 ms=-1/2
The maximum number of electrons in an atom is determined by the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers. The quantum numbers that describe an electron are n, l, ml, and ms. Here, we are given:
Determining the values of ml
The quantum number ml describes the orientation of the electron's orbital in space. For a given value of l, ml can range from -l to +l. In this case, l = 3, so ml can have the following values:
- ml = -3
- ml = -2
- ml = -1
- ml = 0
- ml = +1
- ml = +2
- ml = +3
Determining the number of electrons
Since ms = -1/2, we know that the electron has a spin of "down". This means that we can only place one electron in each orbital with a given set of quantum numbers before we need to start pairing them up. Therefore, the maximum number of electrons that can have n = 4, l = 3, and ms = -1/2 is:
- 1 electron with ml = -3
- 1 electron with ml = -2
- 1 electron with ml = -1
- 1 electron with ml = 0
- 1 electron with ml = +1
- 1 electron with ml = +2
- 1 electron with ml = +3
Therefore, the maximum number of electrons that can have these quantum numbers is 7.