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# What is the total number of electrons in the sixth energy level (n = 6)?

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Energy level is defined with the principal quantum number $n$.

Each level has subshells defined with the azimuthal quantum number $l$.

Each subshell has a different number of orbitals, defined with the magnetic quantum number $m_l$.

Each orbital has two electrons.

So in order to determine the number of electrons, we have to determine the possible values of $l$ and $m_l$.

The azimuthal quantum number $l$ can take the following values:

$l=0,1,2\dots n-1$

The magnetic quantum number $m_l$ can take the following values:

$m_l=l,\dots-l$

We can conclude that the azimuthal quantum number can have $n$ different values $\left("n-1"\right)+\left("0"\right)=n$.

Also, the magnetic quantum number can have $2l+1$ different values: $("l")+("-l")+("0")=2l+1$.

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