# Question #e14cb

Jan 28, 2017

Here's my explanation.

#### Explanation:

The structure of energy shells

A shell consists of all orbitals with the same principal quantum number $n$.

All energy shells except $n = 1$ are made of two or more subshells.

Thus, the $n = 2$ shell consists of the $\text{2s}$ and $\text{2p}$ subshells; the $n = 3$ subshell consists of $\text{3s}$, $\text{3p}$, and $\text{3d}$ subshells, etc.

Subshells in a hydrogen atom

In a hydrogen atom, all the subshells in a shell have the same energy. The number of orbitals and electrons in each subshell is:

$\boldsymbol{\text{Type"color(white)(m)"Orbitals"color(white)(m)"Electrons}}$
$\textcolor{w h i t e}{m l} \text{s} \textcolor{w h i t e}{m m m m l} 1 \textcolor{w h i t e}{m m m m m l l} 2$
$\textcolor{w h i t e}{m l} \text{p} \textcolor{w h i t e}{m m m m l} 3 \textcolor{w h i t e}{m m m m m l l} 6$
$\textcolor{w h i t e}{m l} \text{d} \textcolor{w h i t e}{m m m m l} 5 \textcolor{w h i t e}{m m m m m} 10$
$\textcolor{w h i t e}{m l} \text{f} \textcolor{w h i t e}{m m m m l l} 7 \textcolor{w h i t e}{m m m m m} 14$
$\textcolor{w h i t e}{m l} \text{g} \textcolor{w h i t e}{m m m m l} 9 \textcolor{w h i t e}{m m m m m} 18$

This gives the maximum number of electrons in each shell as 2, 8, 18, 32, 50.

Subshells in other atoms

In atoms with more than one electron, the energies of the subshells change because of repulsions between the electrons. Within a shell, the relative energies are in the order $n \text{s" < n"p" < n"d" < n"f}$, but they get mixed up with the energies of other shells.

Thus, $4 \text{s" < 3"d}$ in energy.

(a) Potassium atoms

A $\text{K}$ atom fills its K and L shells, but the $4 \text{s}$ subshell is lower in energy than the $3 \text{d}$, so it gets filled first.

The number of electrons in each shell becomes, 2, 8, 8, 2 instead of 2, 8, 10.

(b) Tin atoms

An $\text{Sn}$ atom fills its K, L, and M shells, but the $5 \text{s}$ and $5 \text{p}$ subshells are lower in energy than the $4 \text{f}$, so they get filled first.

The number of electrons in each shell becomes, 2, 8, 18, 18, 4 instead of 2, 8, 18, 22.