The principal quantum number \((n)\) has \(n-1\) values of \(l\) including zero. For \(n=3\) :
\(l=0 \quad \rightarrow \quad ' s^{\prime}\) orbital
\(l=1 \rightarrow^{\prime} p^{\prime}\) orbital
\(l=2 \quad \rightarrow \quad d^{\prime}\) orbital
Therefore, the number of sublevels in the \(n=3\) level is 3 . The number of orbitals in \(n\) th level is \(n^{2}\). So, the number of orbitals in the \(n=3\) level is 9 . They are \(3 s, 3 p_{x}, 3 p_{y}, 3 p_{z}, 3 d_{x y}, 3 d_{y z}, 3 d_{x z}, 3 d_{x^{2}-y^{2}}\), and \(3 d_{z^{2}}\)
The maximum number of electrons in \(n\) th level is \(2 n^{2}\). So, the maximum number of electrons in the \(n=3\) level is 18 .
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