Electronic structure makes the periodic table intelligible. Orbitals provide an economical model for where electrons are likely to be found, while ionisation-energy evidence reveals shell structure, subshells and the strength of attraction between a nucleus and its electrons.

A shell contains one or more subshells; a subshell contains orbitals; an orbital holds at most two electrons of opposite spin. The $s$ subshell has one orbital and holds two electrons, $p$ has three orbitals and holds six, and $d$ has five orbitals and holds ten.

Orbitals are probability regions, not fixed circular paths. At this level, describe an $s$ orbital as spherical and a $p$ orbital as two-lobed. The models explain why electrons occupy distinct energy levels and why energy is needed to remove them.

First ionisation energy is the energy needed to remove one electron from each gaseous atom in a mole of atoms, producing gaseous 1+ ions. Successive ionisations remove electrons from increasingly positive ions and therefore generally require more energy. A very large jump marks removal from a lower principal shell after outer electrons are gone. Across a period, nuclear charge, shielding and subshell structure all matter; trends need an explanation rather than a blanket claim of smooth increase.

Fill lower-energy subshells first and use the capacities $s^2$, $p^6$ and $d^{10}$. In electron-in-box notation, place one electron in each equal-energy orbital before pairing them. This minimises electron repulsion and reflects the observed electronic structures.

For elements through krypton, a configuration such as $1s^{2}2s^{2}2p^{6}3s^2$ communicates both shell and subshell occupancy. The outer configuration predicts many chemical properties, so it is more useful than a simple shell notation when explaining periodicity.

Cations form when atoms lose electrons; anions form when atoms gain them. For main-group atoms, add or remove electrons from the outermost occupied shell. For transition-metal ions, remove the $4s$ electrons before the $3d$ electrons because the $4s$ electrons become higher in energy once the atom has electrons in the $3d$ subshell.

Always write the neutral-atom configuration first, then adjust the electron count. The ion's configuration must contain the correct total number of electrons and should be consistent with its stated charge.

The first ionisation-energy equation must show gaseous atoms and gaseous singly charged ions: $\mathrm{X}(\mathrm{g})\to {\mathrm{X}}^{+}(\mathrm{g})+{\mathrm{e}}^{-}$. Ionisation is always endothermic because energy is needed to overcome the attraction between a negative electron and the positive nucleus.

First ionisation energy rises across a period overall because nuclear charge rises while electrons enter the same shell. It falls down a group because increased distance and shielding more than offset the increased nuclear charge. A complete explanation names the changing factor and links it to attraction on the electron removed.

Small dips in the across-period trend are meaningful. Removing a $2p$ electron from boron needs less energy than removing a $2s$ electron from beryllium because the $2p$ electron is higher in energy. Oxygen has a lower first ionisation energy than nitrogen because pairing in one $2p$ orbital increases electron-electron repulsion.

A very large jump between successive ionisation energies shows that all outer-shell electrons have been removed and the next electron comes from an inner shell. The number of electrons removed before the jump therefore identifies the number of valence electrons and often the main group.

Successive ionisation energies are not just a sequence of numbers; they are a record of the changing attraction experienced by each electron removed. The first electron is removed from a neutral atom, the second from a +1 ion, and so on. Each removal makes the remaining electrons more strongly attracted to the nucleus, so successive values generally increase.

A very large jump identifies the point at which removal begins from an inner shell. The number of electrons removed before the jump is therefore the number of outer-shell electrons. Within a shell, a smaller irregularity can arise when removal changes from an s subshell to a higher-energy p subshell, or when pairing begins and electron–electron repulsion makes one electron easier to remove.

Tables and graphs of successive ionisation energies or line spectra can be treated as experimental evidence for shells and subshells. The quality of the conclusion depends on recognising scale changes and comparing like with like.

A trend explanation needs more than naming a factor: show how it changes the attraction between nucleus and electron.