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Due to Pauli exclusion principle, each quantum state can be occupied by no more than one electron in a electron system. However, why there is more than one electron in the same energy level in the energy diagram below? For example in Silicon atom, $2p$ orbital energy level, filled with 6 electrons.

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Perhaps you're confusing quantum state with energy state.

In quantum mechanics, you have the notion of degeneracy: when several quantum states have the same energy, they're said to be degenerate. Or the energy level is said to be degenerate.

In an atom, the quantum state of an electron is defined by a quadruplet of quantum numbers $(n,l,m_l,m_s)$, while energy depends only on $n$ and $l$.

It means that two electrons sharing the same values for $n$ and $l$, but having different $m_l$ and/or $m_s$, will be on the same energy level.

Since $-l\leqslant m_l\leqslant l$, for a given $(n,l)$, there are $2l+1$ possibles values of $m_l$. Since $m_s=\pm 1/2$, you can conclude that a given energy level $(n,l)$ contains $2(2l+1)$ quantum states, i.e. can contain $2(2l+1)$ electrons.

Examples:

  • Any subshell of type $p$ (like $2p$, $3p$...) has $l=1$, so it contains $2(2\times 1+1)=6$ electrons at most.
  • Any subshell of type $d$ has $l=2$, so it contains 10 electrons at most.

And so on.

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