Electron Configuration Calculator

The filling rule predicts; the tables report a measurement

It is easy to assume that a published electron configuration is the output of the aufbau procedure. It is not. Ground-state configurations are experimental results, derived from atomic spectra and compiled by standards bodies from decades of spectroscopic work, and the filling rule is a remarkably good model of those results rather than their source.

That distinction is the reason there are exceptions at all. If configurations were generated by the rule there could be no elements that disobey it; the rule would simply be the definition. What actually happens is that around twenty elements have measured ground states differing from the prediction, and one or two more are argued about.

It also explains why different references disagree about how many exceptions there are. Some counts include only the d-block, some add the actinides, and some heavy elements have configurations that are calculated rather than observed. A source quoting nineteen and a source quoting twenty are usually drawing the boundary in different places rather than contradicting each other.

Why 4s fills first and empties first

The standard classroom explanation — that 4s lies lower in energy than 3d — is the source of a paradox that troubles anyone who thinks about it. If 4s is genuinely lower, why does an iron atom give up its 4s electrons first when it ionises?

The resolution is that an orbital's energy is not a fixed attribute of the element. It shifts with the nuclear charge and, decisively, with which other orbitals already hold electrons. Once 3d begins to fill in the transition series, the 3d level drops below 4s — so in a neutral transition-metal atom, 3d is the lower level, and yet the ground state still has two electrons in 4s.

That sounds contradictory only if you think an atom fills a fixed ladder. It does not. The ground state is whichever whole configuration has the lowest total energy, and total energy includes the mutual repulsion between electrons. The 3d orbitals are compact, so crowding several electrons into them is expensive; parking two in the roomier 4s costs less overall even though 4s is the higher one-electron level. When the atom then ionises, the electrons that leave are the ones furthest out and least tightly bound in the resulting ion — the 4s pair.

So "fill 4s, empty 4s" is not an inconsistency to be memorised around. It is what you get when you stop treating the aufbau sequence as a statement about orbital energies and start treating it as a rule of thumb for finding a minimum-energy arrangement.

The same correction applies to the usual account of the exceptions. Chromium and copper are explained by the extra stability of a half-filled or filled d subshell, which is a reasonable story and an incomplete one. Niobium's ground state is 4d⁴5s¹ — neither half-filled nor filled — and ruthenium's is 4d⁷5s¹. Neither has the tidy subshell the explanation is built on. The honest position is that these configurations come out of the balance between orbital energies and electron repulsion in each specific atom, and the half-filled-shell rule is a useful summary of some of them rather than the reason for any of them.

Four ways to write the same atom

Several notations circulate and they answer different questions, which is why more than one is worth having in front of you at once.

• Filling order lists subshells in the sequence the aufbau rule fills them, so 4s appears before 3d. It shows the reasoning.
• Shell order groups everything by principal quantum number, so 3d appears before 4s. It makes the outermost shell easy to read off, which is what bonding depends on.
• Noble-gas shorthand compresses the closed inner part into a single bracketed symbol. Niobium's [Kr] 4d⁴ 5s¹ says in three terms what the full string needs ten to say, and it leaves the two subshells that actually do chemistry standing on their own.
• Electrons per shell — the 2, 8, 18 style list — is not a configuration at all. It comes from the Bohr model, it still appears on school diagrams and on most printed periodic tables, and it cannot tell you which subshells are occupied. Treat it as a summary of a configuration, never as a substitute for one.

Building lead from its noble-gas core

For a heavy element, walking the entire filling sequence from 1s is slow and error-prone. Reading the configuration off the periodic table's own structure is faster, and it is the method worth practising.

Lead is element 82, in period 6 of the p-block, two columns into it. Start from the noble gas that ends the previous period — xenon, element 54 — and cross period 6 from left to right, picking up each block as you pass through it:

• [Xe] accounts for 54 electrons.
• The f-block of period 6 is filled: 4f¹⁴ takes the running total to 68.
• The d-block is filled: 5d¹⁰ takes it to 78.
• Both s-block columns are behind us: 6s² makes 80.
• Lead is the second element in the p-block, so 6p² makes 82.

Which gives [Xe] 4f¹⁴ 5d¹⁰ 6s² 6p², and the running total arriving exactly at 82 is the check built into the method. The whole calculation is four additions and it works for any element in the table.

The inert pair, and ions that keep their s electrons

Lead is also the clearest illustration of why heavy p-block ions are not what a simple valence argument suggests.

Removing lead's two 6p electrons gives Pb²⁺ at [Xe] 4f¹⁴ 5d¹⁰ 6s² — a cation that has kept a filled s subshell rather than losing it. Pb⁴⁺ exists but is strongly oxidising and much less common in ordinary chemistry. Tin behaves the same way, with Sn²⁺ and Sn⁴⁺ both real but the tetravalent state dominant higher up the group and the divalent state gaining ground lower down. Thallium takes it furthest: Tl⁺ is its stable ion and Tl³⁺ is an oxidant.

This is the inert pair effect, and its origin is not chemical at all. The correction that relativity applies to an s orbital grows steeply with nuclear charge, and at lead it has pulled the 6s level down far enough that ordinary reactions leave the pair alone. The 6p electrons go; the 6s pair stays. A configuration that looks anomalous is a direct fingerprint of relativity in ordinary chemistry.

Past fermium, nobody has measured anything

For roughly the first hundred elements, the configuration you are reading is grounded in spectroscopy. Beyond that, the atoms exist in quantities of a few at a time and for fractions of a second, and the tabulated configurations are the output of relativistic quantum calculations.

Lawrencium, element 103, is the case that made this concrete. By analogy with lutetium directly above it, the expected ground state was [Rn] 5f¹⁴ 7s² 6d¹. Relativistic calculations instead predicted [Rn] 5f¹⁴ 7s² 7p¹, and in 2015 a Japanese-led team at the JAEA tandem accelerator measured lawrencium's first ionisation energy — from a handful of atoms — and found a value consistent with the 7p assignment. That result feeds directly into the long-running argument about which elements belong in group 3.

Even in the actinides, where measurements do exist, the pattern is untidy. Thorium is [Rn] 6d² 7s² and has no 5f electron whatever, despite sitting in the f-block.

Where your source and this one may disagree

Three sources of legitimate disagreement are worth recognising before assuming an error.

A textbook may print the aufbau prediction rather than the measured ground state, particularly for the heavier d-block and the actinides. A table may quote a configuration in shell order while another quotes filling order, which looks like a discrepancy and is only a sorting choice. And for the superheavy elements, two references may quote different calculations.

One last distinction matters when reading spectroscopic data. Every configuration discussed here is a ground state. Excited configurations are perfectly real — helium's 1s¹ 2s¹ is a genuine state of a genuine atom, not a mistake — and atomic spectra are essentially catalogues of them. A configuration also does not fully specify a state: two atoms with identical configurations can sit in different terms depending on how their spins and orbital momenta couple, which is what term symbols exist to record. For predicting chemistry the configuration is enough. For reading a spectrum it is the beginning.