Orbital Diagram Notation

Orbital Diagram Notation

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The orbital diagram (or box diagram) is a visual representation of the electron configuration that shows how electrons are distributed among the specific orbitals within a subshell, including their spin.

Key Rules for Filling the Diagram:

  • Aufbau Principle: fill orbitals starting with the lowest energy level (e.g., 1s before 2s and 4s before 3d);
  • Pauli Exclusion Principle: a maximum of two electrons can occupy a single orbital;
  • Hund's Rule: For degenerate orbitals (orbitals of equal energy, like the three p orbitals), electrons will occupy each orbital singly before pairing up in any one orbital.

The number of individual orbitals (boxes) in a subshell is determined by the angular momentum quantum number (l):

  • s subshell (l=0): 1 orbital (box), 2 electrons maximum;
  • p subshell (l=1): 3 orbitals (boxes), 6 electrons maximum;
  • d subshell (l=2): 5 orbitals (boxes), 10 electrons maximum;
  • f subshell (l=3): 7 orbitals (boxes), 14 electrons maximum.

As an example, let's use the electron configuration for Nitrogen (N), which has 7 electrons: 1s2 2s2 2p3.

  • Identify Orbitals: 1s, 2s, 2p. s orbitals have 1 box, p orbitals have 3 boxes (degenerate);
    • example
  • Fill Lowest Energy (1s2): place two electrons in the 1s orbital;
    • example
  • Fill Next Level (2s2): place two electrons in the 2s orbital;
    • example
  • Fill Degenerate (2p3): place the remaining three electrons into the three 2p orbitals. Crucially, follow Hund's Rule: put one electron in each box first before pairing them up;
    • example
  • Create numerical array notification: "2 2 111".
Note, that the final diagram for Nitrogen clearly shows three unpaired electrons in the 2p subshell, which is information the configuration notation 2p3 alone does not provide.

You will be given the electron configuration of an element in standard notation. You need to create the numerical array representation (electron counts per orbital) of orbital diagram for the sequential orbital terms (without the noble gas core). If necessary, complement the subshell with zeros to represent unoccupied orbitals.

Input: String (str).

Output: String.

Examples: 

assert notation("1s1") == "1"
assert notation("1s2") == "2"
assert notation("[Ne] 3s2 3p1") == "2 100"
assert notation("[He] 2s2 2p4") == "2 211"
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freeman_lex
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