Trace structural subshell assignments for any element or ion in real time.
Quantum Chemistry Lab
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Select an element or enter a total electron count above to begin.
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Full Electron Configuration
Noble Gas Configuration
Valence Electrons
Quantum Numbers of the Differentiating (Last) Electron
n
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Principal
l
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Azimuthal
ml
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Magnetic
ms
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Spin
Valence Orbital Diagram
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Key Terms Explained
Aufbau Principle
The rule that electrons fill orbitals from the lowest energy level upward, following the Madelung order: 1s, 2s, 2p, 3s, 3p, 4s, 3d...
Pauli Exclusion Principle
No two electrons in the same atom can have identical values for all four quantum numbers. Each orbital holds at most 2 electrons with opposite spins.
Hund's Rule
Electrons fill degenerate orbitals (same subshell) one at a time with parallel spins before any orbital is doubly occupied. This minimizes repulsion.
Valence Electrons
Electrons beyond the noble gas core that participate in bonding. They determine an element's chemical reactivity and bonding behavior.
Subshell (s, p, d, f)
A subdivision within a shell defined by azimuthal quantum number l. s holds 2e, p holds 6e, d holds 10e, f holds 14e maximum.
Noble Gas Core
The inner electron configuration represented by the symbol of the preceding noble gas (He, Ne, Ar, Kr, Xe, Rn, Og) in square brackets.
Principal Quantum Number (n)
Defines the electron's shell (energy level). n = 1, 2, 3... As n increases, the electron is farther from the nucleus and has higher energy.
Spin Quantum Number (ms)
Describes the intrinsic angular momentum of an electron: +1/2 (spin up, symbolized by an upward arrow) or -1/2 (spin down, downward arrow).
The Complete Guide to Electron Configurations
Electron configuration describes how electrons are distributed among the atomic orbitals of an element. It governs virtually every chemical property of an atom - from the color of a flame to the bonds it forms to whether it is a metal or a nonmetal.
How to Use This Tool
Use Mode A to look up any of the 118 elements by name, symbol, or atomic number. Type "Fe", "iron", or "26" and the matching element appears instantly. Use Mode B to enter any custom electron count, which is useful for hypothetical or unnamed heavy elements. Adjust the Ion Charge to add or remove electrons and see how ionization shifts the configuration. All outputs update in real time as you type - no button needed.
The Madelung Rule and Filling Order
The standard filling sequence follows the Madelung rule (also called the Aufbau or (n+l) rule). Subshells with a lower (n+l) sum fill first; ties go to the lower n. This gives the familiar diagonal arrow order:
Fill Order
Subshell
n+l
Max Electrons
Cumulative
1
1s
1
2
2
2
2s
2
2
4
3
2p
3
6
10
4
3s
3
2
12
5
3p
4
6
18
6
4s
4
2
20
7
3d
5
10
30
8
4p
5
6
36
9
5s
5
2
38
10
4d
6
10
48
11
5p
6
6
54
12
6s
6
2
56
13
4f
7
14
70
14
5d
7
10
80
15
6p
7
6
86
16
7s
7
2
88
17
5f
8
14
102
18
6d
8
10
112
19
7p
8
6
118
The Known Exceptions
About 20 elements deviate from the Madelung prediction. The most commonly tested are chromium (Cr, Z=24) and copper (Cu, Z=29) in the 4th period, where one electron migrates from 4s to 3d to achieve a half-filled (3d5) or fully-filled (3d10) d subshell. The extra stability comes from maximized exchange energy and reduced electron-electron repulsion. Similar anomalies exist in the 5th period (Nb, Mo, Ru, Rh, Pd, Ag) and throughout the lanthanides and actinides (La, Ce, Gd, Pt, Au, Ac, Th, Pa, U, Np, Cm, Lr). This solver uses a hardcoded override map for all known exceptions, ensuring scientifically accurate output for every element.
Ion Configuration and the Removal Order
When an atom loses electrons (cation) or gains electrons (anion), the configuration changes. A key rule for transition metals: even though 4s fills before 3d, electrons are removed from 4s first when forming cations. This is because once the 3d orbitals are occupied, orbital contraction makes 3d lower in energy than 4s. Iron (Z=26, [Ar] 3d6 4s2) forms Fe2+ as [Ar] 3d6, not [Ar] 3d4 4s2. The ion adjuster in this solver removes from the highest principal quantum number shell first, which is the experimentally correct behavior.
Reading the Quantum Numbers
The four quantum numbers together completely specify the state of an electron. n gives the shell. l gives the subshell shape (0=s, 1=p, 2=d, 3=f). ml gives the specific orbital within that subshell, ranging from -l to +l. ms gives spin: the first electron in any orbital gets ms = +1/2, the pairing electron gets ms = -1/2. This tool displays the quantum numbers for the differentiating electron - the last one added to reach the current configuration.
Frequently Asked Questions
Chromium ([Ar] 3d5 4s1) and copper ([Ar] 3d10 4s1) deviate from the Madelung prediction because a half-filled or fully-filled d subshell is especially stable. In chromium, the system lowers its overall energy by promoting one electron from 4s to 3d, achieving a half-filled 3d5 configuration. In copper, one electron moves from 4s to 3d to complete the full 3d10 set. Both configurations reduce electron-electron repulsion and maximize exchange energy - the quantum mechanical benefit of having parallel spins across the same subshell. Similar reasoning explains anomalies in molybdenum, palladium, silver, gold, platinum, and many lanthanides and actinides.
A shell is defined by the principal quantum number n (n = 1, 2, 3...) and represents a general energy level. Each shell contains one or more subshells. A subshell is defined by both n and the azimuthal quantum number l (s, p, d, f). For example, the third shell (n=3) contains three subshells: 3s, 3p, and 3d. Each subshell contains orbitals (2l+1 per subshell), and each orbital holds at most 2 electrons. So the 3d subshell has 5 orbitals and can hold up to 10 electrons.
When building up configurations, 4s fills before 3d because it has lower energy at that stage. But once 3d orbitals are occupied, electron-electron interactions and orbital contraction cause the 3d orbitals to drop below 4s in energy. So when ionization removes electrons, they come from the highest-n shell first (4s before 3d), which is the experimentally confirmed behavior. Iron (Fe) has [Ar] 3d6 4s2 as a neutral atom, but Fe2+ is [Ar] 3d6, not [Ar] 3d4 4s2. Fe3+ continues to [Ar] 3d5.
n is the shell number of the last-filled subshell. l is the subshell type: 0 for s, 1 for p, 2 for d, 3 for f. ml is the magnetic quantum number of the specific orbital that received the last electron; it ranges from -l to +l, with orbitals filled from -l upward (Hund's Rule applies - each orbital gets one electron before doubling up). ms is +1/2 for the first electron entering an orbital, and -1/2 for the pairing electron. Together, these four numbers uniquely identify the quantum state of every electron in the atom.
The Aufbau Principle states that electrons fill orbitals starting from the lowest energy level, following the Madelung (n+l) rule. It works correctly for about 98 of the 118 elements. It fails for roughly 20 elements, primarily in the d-block (transition metals) and f-block (lanthanides and actinides). In these cases, the predicted configuration has higher energy than an alternative arrangement. The exceptions always involve moving electrons to or from the s subshell to achieve a half-filled or fully-filled d or f subshell. This tool overrides the algorithm for all known exceptions.
Valence electrons are those beyond the noble gas core that are involved in chemical bonding. For main-group elements, they occupy the highest principal shell. For transition metals, they include the outermost s electrons and any partially filled d subshell. Elements in the same group of the periodic table have the same number of valence electrons, which is why they share similar chemical behavior. The number of valence electrons predicts oxidation states, bond types, and reactivity - a carbon atom with 4 valence electrons forms 4 bonds, while chlorine with 7 valence electrons tends to gain 1 electron to form a stable octet.