Electron Configuration Calculator

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madelung rule filling order

Madelung rule: filling order and how to apply it

The Madelung diagram is a filling rule: it says in which order subshells receive electrons. You just follow the diagonals and respect each subshell's limit, and the tool draws the diagram marking where each electron ended up.

The order of the diagonals and the limit of each subshell

The order comes from sorting subshells by the sum n + ℓ (ℓ is 0, 1, 2 and 3 for s, p, d and f) and, on a tie, by the lower n: 1s (n + ℓ = 1), 2s (2), 2p and 3s (3), 3p and 4s (4), 3d, 4p and 5s (5), 4d, 5p and 6s (6), 4f, 5d, 6p and 7s (7), 5f, 6d and 7p (8). Each group is a diagonal of the diagram. The limits are 2 electrons in s, 6 in p, 10 in d and 14 in f, and shell n holds at most 2n² (K 2, L 8, M 18, N 32). This explains why 4s fills before 3d: 4 + 0 = 4 is lower than 3 + 2 = 5.
The procedure has three steps. First, the atomic number Z gives the number of electrons in the neutral atom. Second, fill the subshells in order until the electrons run out: sodium (Z = 11) is 1s2 2s2 2p6 3s1, chlorine (Z = 17) is 1s2 2s2 2p6 3s2 3p5 and iron (Z = 26) is 1s2 2s2 2p6 3s2 3p6 4s2 3d6. Third, add up by shell: iron has K = 2, L = 2 + 6 = 8, M = 2 + 6 + 6 = 14 and N = 2, and the last shell (N, with 2 electrons) is the valence shell. Noble gas notation replaces the start with the previous gas: [Ar] 4s2 3d6.
There are two ways to write the same configuration, and Brazilian books use both. In energy order (the diagram's), iron is ... 4s2 3d6; in shell order, ... 3d6 4s2. Both describe the same atom, and the tool has a switch to toggle. In periods 6 and 7 the diagram reaches many more subshells: uranium (Z = 92) comes out as [Rn] 7s2 5f3 6d1 and has 7 shells, K to Q, with 2, 8, 18, 32, 21, 9 and 2 electrons. The data for neutral elements comes from the NIST ground-state table, which matters because 20 elements break the rule.

Configurations by the diagram order

Sodium, Z = 11

Input: Na
Expected output: [Ne] 3s1

One electron in shell M; K = 2, L = 8, M = 1.

Chlorine, Z = 17

Input: Cl
Expected output: [Ne] 3s2 3p5

Seven electrons in the valence shell; K = 2, L = 8, M = 7.

Iron, Z = 26

Input: Fe
Expected output: [Ar] 4s2 3d6

K = 2, L = 8, M = 14, N = 2; 4s comes before 3d.

Bromine, Z = 35

Input: Br
Expected output: [Ar] 4s2 3d10 4p5

K = 2, L = 8, M = 18, N = 7.

Tin, Z = 50

Input: Sn
Expected output: [Kr] 5s2 4d10 5p2

5s fills before 4d: 5 + 0 = 5 against 4 + 2 = 6.

Uranium, Z = 92

Input: U
Expected output: [Rn] 7s2 5f3 6d1

Seven shells, K to Q, with 2, 8, 18, 32, 21, 9 and 2 electrons.

Full tool FAQ

How do you write the electron configuration of an element?

Take the atomic number (the number of electrons in the neutral atom) and distribute them over the subshells in Madelung order, filling each to its maximum (s 2, p 6, d 10, f 14). For chlorine (Z = 17): 1s2 2s2 2p6 3s2 3p5, or [Ne] 3s2 3p5, with 2, 8 and 7 electrons in shells K, L and M.

What is the filling order of the Madelung diagram?

What are the exceptions to the filling order?

How do you write the configuration of an ion?

What are the valence shell and the highest-energy subshell?

How do you find the quantum numbers of the last electron?

What is Hund's rule and what is paramagnetism?

What does [Ar] 4s2 3d6 mean?

How do you know how many electrons each shell has?

Where does the data come from, and does it cover 109 to 118?

Frequently asked questions

Why does 4s fill before 3d?

Because the n + ℓ sum of 4s (4) is lower than that of 3d (5), and that is the ordering criterion of the diagram. Physically, the 4s orbital penetrates closer to the nucleus and has lower energy in the neutral atom when 3d is empty, but the order can reverse once 3d fills.

Do energy order and shell order give different configurations?

They give the same configuration written in different sequences. Iron: 1s2 2s2 2p6 3s2 3p6 4s2 3d6 in energy order and 1s2 2s2 2p6 3s2 3p6 3d6 4s2 in shell order. The highest-energy subshell is 3d in both.

Does the diagram work for every element?

For most, yes, but 20 elements up to hassium have a different ground state, such as chromium and copper. The tool uses the measured data and flags each exception.

Next steps

The order of the diagonals and the limit of each subshell

The order comes from sorting subshells by the sum n + ℓ (ℓ is 0, 1, 2 and 3 for s, p, d and f) and, on a tie, by the lower n: 1s (n + ℓ = 1), 2s (2), 2p and 3s (3), 3p and 4s (4), 3d, 4p and 5s (5), 4d, 5p and 6s (6), 4f, 5d, 6p and 7s (7), 5f, 6d and 7p (8). Each group is a diagonal of the diagram. The limits are 2 electrons in s, 6 in p, 10 in d and 14 in f, and shell n holds at most 2n² (K 2, L 8, M 18, N 32). This explains why 4s fills before 3d: 4 + 0 = 4 is lower than 3 + 2 = 5.

The procedure has three steps. First, the atomic number Z gives the number of electrons in the neutral atom. Second, fill the subshells in order until the electrons run out: sodium (Z = 11) is 1s2 2s2 2p6 3s1, chlorine (Z = 17) is 1s2 2s2 2p6 3s2 3p5 and iron (Z = 26) is 1s2 2s2 2p6 3s2 3p6 4s2 3d6. Third, add up by shell: iron has K = 2, L = 2 + 6 = 8, M = 2 + 6 + 6 = 14 and N = 2, and the last shell (N, with 2 electrons) is the valence shell. Noble gas notation replaces the start with the previous gas: [Ar] 4s2 3d6.

There are two ways to write the same configuration, and Brazilian books use both. In energy order (the diagram's), iron is ... 4s2 3d6; in shell order, ... 3d6 4s2. Both describe the same atom, and the tool has a switch to toggle. In periods 6 and 7 the diagram reaches many more subshells: uranium (Z = 92) comes out as [Rn] 7s2 5f3 6d1 and has 7 shells, K to Q, with 2, 8, 18, 32, 21, 9 and 2 electrons. The data for neutral elements comes from the NIST ground-state table, which matters because 20 elements break the rule.

Configurations by the diagram order

Sodium, Z = 11

Input: Na
Expected output: [Ne] 3s1

One electron in shell M; K = 2, L = 8, M = 1.

Chlorine, Z = 17

Input: Cl
Expected output: [Ne] 3s2 3p5

Seven electrons in the valence shell; K = 2, L = 8, M = 7.

Iron, Z = 26

Input: Fe
Expected output: [Ar] 4s2 3d6

K = 2, L = 8, M = 14, N = 2; 4s comes before 3d.

Bromine, Z = 35

Input: Br
Expected output: [Ar] 4s2 3d10 4p5

K = 2, L = 8, M = 18, N = 7.

Tin, Z = 50

Input: Sn
Expected output: [Kr] 5s2 4d10 5p2

5s fills before 4d: 5 + 0 = 5 against 4 + 2 = 6.

Uranium, Z = 92

Input: U
Expected output: [Rn] 7s2 5f3 6d1

Seven shells, K to Q, with 2, 8, 18, 32, 21, 9 and 2 electrons.

Full tool FAQ

How do you write the electron configuration of an element?

What is the filling order of the Madelung diagram?

What are the exceptions to the filling order?

How do you write the configuration of an ion?

What are the valence shell and the highest-energy subshell?

How do you find the quantum numbers of the last electron?

What is Hund's rule and what is paramagnetism?

What does [Ar] 4s2 3d6 mean?

How do you know how many electrons each shell has?

Where does the data come from, and does it cover 109 to 118?

Frequently asked questions

Why does 4s fill before 3d?

Do energy order and shell order give different configurations?

Does the diagram work for every element?

For most, yes, but 20 elements up to hassium have a different ground state, such as chromium and copper. The tool uses the measured data and flags each exception.