Electronic Configuration of Atoms

2.6.5 Electronic Configuration of Atoms

The distribution of electrons among the various orbitals of an atom is called its electronic configuration. This is not a random assignment — it follows a strict set of rules that arise from the quantum mechanical model of the atom. Once you understand these rules, you can write the electronic configuration of any element systematically.

Two Ways to Represent Electronic Configuration

The textbook presents two standard notations for writing electronic configurations.

The $s^a p^b d^c \dots$ notation — Here, the subshell is identified by its letter symbol ($s$, $p$, $d$, $f$), and the number of electrons in that subshell is written as a superscript. The principal quantum number is written before the subshell symbol to distinguish the same subshell in different shells. For example, $1s^2$ means the first shell ($n=1$), $s$ subshell, containing 2 electrons.

The orbital diagram notation — Each orbital of a subshell is represented by a box (or a line), and each electron is represented by an arrow. An upward arrow ($\uparrow$) indicates an electron with positive spin ($m_s = +\frac{1}{2}$), and a downward arrow ($\downarrow$) indicates an electron with negative spin ($m_s = -\frac{1}{2}$).

Building Up from Hydrogen

The simplest atom is hydrogen, with just one electron. This electron occupies the orbital of lowest energy, which is $1s$. Its electronic configuration is written as $1s^1$.

Helium has two electrons. Both can occupy the $1s$ orbital, giving the configuration $1s^2$. The two electrons must have opposite spins — this is a consequence of the Pauli exclusion principle, which we will discuss shortly. In the orbital diagram, this appears as one $\uparrow$ and one $\downarrow$ in the same box.

Lithium has three electrons. The third electron cannot enter the $1s$ orbital because that orbital is already full (it can hold at most two electrons). The next available orbital of lowest energy is $2s$. So the configuration of lithium is $1s^2 2s^1$.

Beryllium has four electrons. The $2s$ orbital can hold one more electron, giving $1s^2 2s^2$.

Filling the $2p$ Orbitals

From boron (atomic number 5) to neon (atomic number 10), the $2p$ orbitals are progressively filled:

Notice that the $2p$ subshell has three orbitals ($2p_x$, $2p_y$, $2p_z$), each capable of holding two electrons, for a total of six electrons. The filling follows Hund's rule: electrons occupy each orbital singly before pairing begins. So in nitrogen, each of the three $2p$ orbitals gets one electron (all with parallel spins), giving the half-filled $2p^3$ configuration. In oxygen, one orbital gets a second electron (paired), giving $2p^4$, and so on.

The Pattern Repeats: Sodium to Argon

The elements from sodium (Na, atomic number 11) to argon (Ar, atomic number 18) follow exactly the same pattern as lithium to neon, but with the $3s$ and $3p$ orbitals being filled instead of $2s$ and $2p$.

Sodium: $1s^2 2s^2 2p^6 3s^1$

Magnesium: $1s^2 2s^2 2p^6 3s^2$

Aluminium: $1s^2 2s^2 2p^6 3s^2 3p^1$

...

Argon: $1s^2 2s^2 2p^6 3s^2 3p^6$

Core Electrons and Valence Electrons

A useful shorthand is to represent the completely filled inner shells by the symbol of the corresponding noble gas in square brackets. For example, the configuration of sodium can be written as $[\text{Ne}] 3s^1$, where $[\text{Ne}]$ stands for $1s^2 2s^2 2p^6$.

The electrons in the completely filled inner shells are called core electrons. The electrons that are added to the outermost shell (the shell with the highest principal quantum number) are called valence electrons. For the elements sodium through argon, the core electrons are those of neon, and the valence electrons are those in the $3s$ and $3p$ orbitals.

The $4s$ Orbital Fills Before $3d$

In potassium (K, atomic number 19) and calcium (Ca, atomic number 20), something interesting happens. The $4s$ orbital has lower energy than the $3d$ orbitals. Therefore, the 19th electron in potassium goes into $4s$, not $3d$. The configuration of potassium is $[\text{Ar}] 4s^1$, and calcium is $[\text{Ar}] 4s^2$.

The Transition Series: Scandium to Zinc

Beginning with scandium (Sc, atomic number 21), a new pattern emerges. The $3d$ orbital, being lower in energy than the $4p$ orbital, is filled next. So in the ten elements from scandium to zinc, the five $3d$ orbitals are progressively occupied.

Exceptions: Chromium and Copper

You may notice that chromium and copper do not follow the expected pattern. Based on the position in the periodic table, one might expect chromium to be $[\text{Ar}] 3d^4 4s^2$ and copper to be $[\text{Ar}] 3d^9 4s^2$. Instead, chromium is $[\text{Ar}] 3d^5 4s^1$ and copper is $[\text{Ar}] 3d^{10} 4s^1$.

The reason is that half-filled and completely filled subshells have extra stability (lower energy). The configurations $d^5$ (half-filled) and $d^{10}$ (completely filled) are particularly stable. In chromium, one electron from the $4s$ orbital shifts to the $3d$ orbital to achieve the half-filled $3d^5$ configuration. In copper, one electron shifts from $4s$ to $3d$ to achieve the completely filled $3d^{10}$ configuration.

Continuing the Pattern: Gallium to Krypton

After the $3d$ orbitals are saturated at zinc, the filling of the $4p$ orbitals begins at gallium (Ga, $[\text{Ar}] 3d^{10} 4s^2 4p^1$) and is complete at krypton (Kr, $[\text{Ar}] 3d^{10} 4s^2 4p^6$).

The Next Periods: Rubidium to Xenon

In the next eighteen elements from rubidium (Rb, atomic number 37) to xenon (Xe, atomic number 54), the pattern of filling the $5s$, $4d$, and $5p$ orbitals is similar to that of $4s$, $3d$, and $4p$ orbitals. The $5s$ orbital fills first, then the $4d$ orbitals, and finally the $5p$ orbitals.

The Sixth and Seventh Periods …