What is the max number of electrons in an atom that can have the quantum number: n=2, ms= -1/2
A weird question in my opinion but I may have interpreted the question in the wrong way. I'm assuming that if you have anything with n = 2 you must have something in n = 1 also.
You can have 2 electrons in n = 1 but only one of them can have ms = -1/2.
You can have 8 electrons in n = 2 but only half of those can have ms = -1/2
To determine the maximum number of electrons in an atom that can have a given set of quantum numbers, you need to understand the electron configuration and how the quantum numbers relate to it.
The electron configuration describes the arrangement of electrons in the various energy levels or orbitals of an atom. It is usually represented using the notation: 1s² 2s² 2p⁶ and so on.
The first quantum number, known as the principal quantum number (n), represents the energy level or shell of an electron. In this case, n = 2.
The second quantum number, known as the magnetic quantum number (mₛ), describes the orientation or spin of an electron. The possible values for mₛ are +1/2 and -1/2.
According to the Pauli exclusion principle, each electron in an atom must have a unique set of quantum numbers. This means that no two electrons in an atom can have the same set of quantum numbers.
In this case, the given quantum numbers are n = 2 and mₛ = -1/2. The principal quantum number (n) indicates the energy level, so n = 2 means the electron is in the second energy level. The magnetic quantum number (mₛ) signifies the electron's spin, and mₛ = -1/2 indicates a specific spin orientation.
Since only one set of quantum numbers is given, we can conclude that there is only one electron with the quantum numbers n = 2 and mₛ = -1/2.
Overall, the maximum number of electrons in an atom with the quantum number n = 2 and mₛ = -1/2 is one.