Atomic Structure: Question 4

Worked solution

Part (a): Full electronic configuration of phosphorus

Phosphorus has proton number 15, so a neutral atom has 15 electrons. Filling the sub-shells in order of increasing energy ($1s$, $2s$, $2p$, $3s$, $3p$, …), each up to its maximum capacity where possible:

$1s^2\,2s^2\,2p^6\,3s^2\,3p^3$

Check the total: $2+2+6+2+3 = 15$ ✓, matching the proton number.

Part (b): Hund’s rule in the 3p sub-shell

The outermost occupied sub-shell, $3p$, contains three orbitals of equal energy ($3p_x$, $3p_y$, $3p_z$) and three electrons to place in them. The rule that governs how they are arranged is Hund’s rule (the rule of maximum multiplicity): electrons occupy separate orbitals of equal energy singly, with parallel (unpaired) spins, before any orbital receives a second electron.

This happens because electrons are all negatively charged and repel one another. Placing each electron in its own $3p$ orbital keeps the three electrons, on average, further apart in space than would be the case if two of them were forced to share a single orbital while a third orbital stayed empty. Less electron-electron repulsion means lower overall energy, so the singly-occupied, parallel-spin arrangement is the more stable, ground-state configuration.

Part (c): The phosphide ion, P³⁻

The phosphide ion $\text{P}^{3-}$ has gained three extra electrons compared with the neutral atom:

$\text{electrons in P}^{3-} = 15 + 3 = 18$

Continuing to fill sub-shells in order from the neutral atom’s configuration, the $3p$ sub-shell (currently $3p^3$) fills up to its maximum of six before any new sub-shell would be needed:

$1s^2\,2s^2\,2p^6\,3s^2\,3p^6$

Check: $2+2+6+2+6 = 18$ ✓.

This is exactly the electronic configuration of the noble gas argon (proton number 18). $\text{P}^{3-}$ is described as isoelectronic with argon, since both species have the same number and arrangement of electrons, even though they have different numbers of protons.

Final answers

• (a) $\boxed{1s^2\,2s^2\,2p^6\,3s^2\,3p^3}$
• (b) Hund’s rule: the three $3p$ electrons occupy separate orbitals with parallel spins, minimising electron-electron repulsion.
• (c) $\boxed{1s^2\,2s^2\,2p^6\,3s^2\,3p^6}$, the same configuration as argon.