Question

How many orbitals are there in the third shell ($\mathrm{n}=3$)?

Answer 1

The number of orbitals in the third shell:

• In any shell,

$\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{orbitals}={\mathrm{n}}^2$

Where $n$= principal quantum number or shell number

• In the third shell, the principal quantum number is $3$.

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{orbitas}\mathrm{in}\mathrm{third}\mathrm{shell}=3^2 \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{orbitas}\mathrm{in}\mathrm{third}\mathrm{shell}=9 \end{gathered}$$

• Also, the third shell contains three subshells,$3\mathrm{s},3\mathrm{p},3\mathrm{d}$. In which $\mathrm{s}$ subshell has one orbital, $\mathrm{p}$ subshell contains three orbitals, and $\mathrm{d}$subshell is composed of five orbitals. Therefore, $\mathrm{total}\mathrm{}\mathrm{number}\mathrm{}\mathrm{of}\mathrm{}\mathrm{orbitals}\mathrm{}\mathrm{in}\mathrm{}\mathrm{third}\mathrm{}\mathrm{shell}=\; 1+3+5\; =9$

Hence, there are total 9 orbitals in the third shell.