A neutral atom of an element has exactly electrons in the K shell, electrons in the L shell, electro — Atomic Structure Chemistry Question
Question
A neutral atom of an element has exactly $2$ electrons in the K shell, $8$ electrons in the L shell, $8$ electrons in the M shell, and $2$ electrons in the N shell. Calculate the absolute total number of electrons in this atom that simultaneously possess a magnetic quantum number $m = 0$ AND a spin quantum number $s = +1/2$.
💡 Solution & Explanation
The shell distribution corresponds to Calcium ($Z=20$): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2$. We must count electrons with $m = 0$ and $s = +1/2$. Each completely filled orbital contains exactly one electron with $s = +1/2$. Orbitals with $m = 0$ are the $s$ -orbitals and exactly one of the $p$ -orbitals ($p_z$) in each $p$ -subshell. These are: $1s$ ($1e^-$), $2s$ ($1e^-$), $2p$ ($1e^-$ from $m=0$), $3s$ ($1e^-$), $3p$ ($1e^-$ from $m=0$), and $4s$ ($1e^-$). The total number of such electrons is $1+1+1+1+1+1 = 6$.