The statement "each electron in an atom must have its own unique set of quantum numbers" is from the Pauli exclusion principle.
According to the Pauli exclusion principle, two electrons in an atom cannot have the four quantum numbers (n, l, [tex]m_{l}[/tex], [tex]m_{s}[/tex]) equals. These quantum numbers are:
- n: is the principal quantum number, which varies from 1 to 7.
- l: is the azimuthal quantum number, which varies from 0 to n-1. The values of 0, 1, 2, and 3 correspond to the shells s, p, d, and f, respectively.
- [tex]m_{l}[/tex]: is the magnetic quantum number, which goes from -l to +l (going through zero).
- [tex]m_{s}[/tex]: is the spin quantum number, whose values are +1/2 (spin up) and -1/2 (spin down).
For example, for the electronic configuration 3s², the quantum numbers are:
- [tex]m_{s}[/tex] = +1/2 for the first electron and -1/2 for the second, beacuse they cannot be the same (Pauli exclusion principle).
Therefore, each electron in an atom must have its own unique set of quantum numbers is a statement of the Pauli exclusion principle.
You can learn more about the Pauli exclusion principle here:
- https://brainly.com/question/7969824?referrer=searchResults
- https://brainly.com/question/10386902?referrer=searchResults
I hope it helps you!
