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, andm_s or equivalentlys , 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 ancolor(blue)(s) orbital, which contains1 orbit; [2]l=1 corresponds to ap orbital that holds3 orbits;l=2 corresponds to ad orbital which holds5 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/