# Total electrons with quantum number n=4 l=1 s=-1/2?

##### 1 Answer

Three.

#### Explanation:

Each electron has a set of four atomic quantum numbers: [1]

#n# , the principal quantum number,#l# , the orbital angular momentum quantum number,#m_l# , the magnetic quantum number, and#m_s# or equivalently#s# , the electron spin quantum number.

By the Pauli Exclusion Principle, each electron in an atom shall have a unique set of the four quantum numbers. Therefore, the number of quantum number values combinations possible determines the number of electrons satisfying such conditions.

The question gives the value of three out of the four quantum numbers:

#n=4# ;#l=1# ;#color(darkblue)(m_l)# is yet to be determined;#m_s=1/2#

#m_l-l,-l+1, -l+2, ... , -1, 0, 1, 2, ..., l-1, l#

and therefore has

**Alternative Explanation**

Here's an alternative approach that does not require knowledge about the connection between

The

#l=color(blue)(0)# corresponds to an#color(blue)(s)# orbital, which contains#1# orbit; [2]#l=1# corresponds to a#p# orbital that holds#3# orbits;#l=2# corresponds to a#d# orbital which holds#5# orbits;

and so on so forth.

The Pauli's Exclusion Principle suggests that the two electrons in a single electron orbit shall have the opposite spins,

A

**References**

[1] Kamenko, Anastasiya, et. al, "Quantum Numbers", https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/10%3A_Multi-electron_Atoms/Quantum_Numbers

[2] "Quantum Numbers", https://www.ck12.org/chemistry/quantum-numbers/lesson/Quantum-Numbers-CHEM/