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4 months ago in Quantum Mechanics By Phoebe

Did the 2n² rule trick generations of physics students?

I remember learning that electron shells fill according to 2n². Then I got to transition metals and everything fell apart. Was this formula just a convenient lie?

AtomicStructure

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By Suma Answered 1 month ago

It wasn't a lie—it was just incomplete. 2n² gives the maximum capacity of a shell, which is a real quantum mechanical result from the Pauli Exclusion Principle. What it doesn't tell you is the order of filling, because subshells (s, p, d, f) have different energies that overlap across shells. The formula wasn't fooling anyone; it was just the first chapter, not the whole book.

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