# An atom contains a total of 25 electrons. When the atom is in the ground state, how many different principal energy levels will contain electrons?

Jan 18, 2018

Well, with $25$ electrons, whatever atom it is, it need not be neutral... but since it's within the neighborhood of a transition metal, we can assume it's one of them... i.e. it may be $\text{Mn}$, or perhaps ${\text{Co}}^{2 +}$.

With $25$ electrons, we can immediately write the electron configuration. Argon has $18$ electrons and is the previous noble gas, and thus we use it as the noble gas core.

$1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {s}^{2} 3 {p}^{6} 3 {d}^{5} 4 {s}^{2} \to \left[A r\right] 3 {d}^{5} 4 {s}^{2}$

And you can convince yourself that $18 + 5 + 2 = 25$ electrons total.

This lands us in the first-row transition metals, and so we have involved $\boldsymbol{n = 1 , 2 , 3 ,}$ and $\boldsymbol{n = 4}$. Those are the only principal energy levels involved... These contain the following orbitals:

$n = 1$: $1 s$
$n = 2$: $2 s , 2 p$
$n = 3$: $3 s , 3 p , 3 d$
$n = 4$: $4 s$

We ignore the $4 p , 4 d , 4 f$ obviously because they are empty.