7.4.6. Electron Shells

Table of Contents

Basic idea

Electron shells are the allowed groups of energy levels where electrons can be found around an atom’s nucleus. Instead of moving in any orbit at any energy, electrons in atoms occupy specific energy arrangements. These arrangements are organized into shells, which help us describe how electrons are distributed and why different atoms behave differently in chemistry and spectroscopy.

A shell is mainly identified by the principal quantum number $n$. The first shell is $n=1$, the second is $n=2$, the third is $n=3$, and so on. Shells farther from the nucleus generally correspond to higher electron energy and larger average distance from the nucleus.

Shell labels

Historically, shells are also labeled by letters:

Principal quantum number	Shell label
$n=1$	K
$n=2$	L
$n=3$	M
$n=4$	N
$n=5$	O

So the K shell is the innermost shell, and the L shell is the next one outside it.

A shell is defined by the principal quantum number $n$.
Small $n$ means lower energy and, on average, closer to the nucleus.

Shells and subshells

Each shell contains one or more subshells. These subshells are labeled $s$, $p$, $d$, and $f$. The shell number tells us which subshells are possible.

For example, in the shell $n=1$, only the $1s$ subshell exists. In the shell $n=2$, there are $2s$ and $2p$ subshells. In the shell $n=3$, there are $3s$, $3p$, and $3d$ subshells.

Shell	Possible subshells
$n=1$	$1s$
$n=2$	$2s$, $2p$
$n=3$	$3s$, $3p$, $3d$
$n=4$	$4s$, $4p$, $4d$, $4f$

Shells are broad groupings, while subshells provide a more detailed structure inside each shell.

Capacity of a shell

A shell can hold only a limited number of electrons. The maximum number in shell $n$ is

$$
N_{\max} = 2n^2
$$

This gives:

Shell	$n$	Maximum electrons
K	1	2
L	2	8
M	3	18
N	4	32

For instance, the first shell can hold at most 2 electrons, and the second shell can hold at most 8 electrons.

Maximum electrons in shell $n$:
$$
N_{\max} = 2n^2
$$

Why shells matter

Electron shells strongly affect atomic behavior. The electrons in the outermost shell are especially important, because they are less tightly bound than inner electrons. These outer electrons are often the ones involved in atomic interactions and radiation processes.

Inner shells are usually filled first because they have lower energy. When an inner-shell electron is removed, for example by a high energy collision or incoming radiation, an electron from a higher shell can fall into the empty place. This change can produce electromagnetic radiation, often in the X ray region.

Shell transitions

If an electron moves from a higher shell to a lower shell, the atom loses energy. That energy is emitted as a photon. If an electron absorbs the right amount of energy, it can jump from a lower shell to a higher shell.

The energy of the emitted or absorbed photon satisfies

$$
E_{\gamma} = E_i - E_f
$$

for a transition from an initial energy level $E_i$ to a lower final energy level $E_f$, where $E_i > E_f$.

A transition ending in the K shell is especially energetic because the K shell is very close to the nucleus and has low energy. This is why K shell X rays are important in atomic physics.

When an electron changes shells, the photon energy equals the difference in atomic energy levels:
$$
E_{\gamma} = \Delta E
$$
Only specific shell differences are allowed, so only specific photon energies appear.

Hydrogen as a simple example

The hydrogen atom is the simplest case because it has only one electron. Its allowed shell energies are

$$
E_n = -\frac{13.6\ \text{eV}}{n^2}
$$

So the first few energies are:

Shell	$n$	Energy
1st	1	$-13.6\ \text{eV}$
2nd	2	$-3.4\ \text{eV}$
3rd	3	$-1.51\ \text{eV}$

The negative sign means the electron is bound to the nucleus. Higher shells have energies closer to zero, so the electron is less tightly bound.

Although many-electron atoms are more complicated, the shell idea still remains very useful.

Inner and outer shells

Electrons in inner shells are usually more strongly attracted to the nucleus. Electrons in outer shells are, on average, farther away and are more easily removed. The energy needed to remove an electron from an atom is related to how strongly that electron is bound.

In heavy atoms, inner shell electrons can remain very tightly bound, while outer shell electrons may be comparatively weakly bound. This difference helps explain why atoms can emit high energy photons from inner-shell transitions and lower energy photons from outer-shell transitions.

A visual picture

Rendering scientific sketch…

Electron shells around a nucleus

This drawing is only a schematic picture. Real electrons are not tiny planets moving on fixed circular tracks. Shells are better understood as allowed quantum states with characteristic energies.

Connection to atomic structure

The shell model gives a first organized picture of how electrons are arranged in atoms. It explains why atoms have layered structure, why only certain energies are allowed, and why atoms emit or absorb discrete spectral lines. A more complete description also uses subshells and orbitals, but the shell idea is the starting point.

Electron shells are not arbitrary distances from the nucleus. They are quantized energy groupings.
This quantization is why atoms absorb and emit only specific photon energies.

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