The total number of orbitals associated with the principal quantum number $\mathrm{n}=3$ is:

1. Bohr’s model of atom:

(i) Frequency of radiation absorbed or emitted during transition: $\mathrm{v}=\frac{\mathrm{\Delta E}}{\mathrm{h}}\mathrm{=}\frac{{\mathrm{E}}_{\mathrm{2}}-{\mathrm{E}}_{\mathrm{1}}}{\mathrm{h}}$

(ii) Quantization of angular momentum: $\mathrm{mvr}=\mathrm{n}\frac{\mathrm{h}}{2\mathrm{\pi }}$

(iii) Energy of stationary states: ${\mathrm{E}}_{\mathrm{n}}\mathrm{=}-\frac{21.8{\times 10}^{-\mathrm{19}}}{{\mathrm{n}}^{\mathrm{2}}}{\mathrm{Z}}^{\mathrm{2}}\hspace{0.17em}\mathrm{J}\hspace{0.17em}{\mathrm{atom}}^{-1}$

(iv) Radii of the stationary orbits: ${\mathrm{r}}_{\mathrm{n}}=52.9\times \left(\frac{{\mathrm{n}}^{\mathrm{2}}}{\mathrm{Z}}\right)\mathrm{pm}$

(v) Energy gap between two orbits: $\mathrm{\Delta E}={\mathrm{R}}_{\mathrm{H}}\left(\frac{\mathrm{1}}{{\mathrm{n}}_{\mathrm{i}}^{\mathrm{2}}}-\frac{\mathrm{1}}{{\mathrm{n}}_{\mathrm{f}}^{\mathrm{2}}}\right)$

Where, ${\mathrm{n}}_{\mathrm{i}}$ and ${\mathrm{n}}_{\mathrm{f}}$ are initial orbit and final orbit respectively.

2. De Broglie relation:

de Broglie relation is $\mathrm{\lambda } = \mathrm{h}/\mathrm{mv} = \mathrm{h}/\mathrm{p}$ where λ is wavelength, m is mass, v is velocity and p is momentum of the material particle.

3. Heisenberg's uncertainty principle:

$\mathrm{\Delta x}.\mathrm{\Delta p}>\frac{\mathrm{h}}{4\mathrm{\pi }}\text{ or }\mathrm{m\Delta x}.\mathrm{\Delta v}\ge \frac{\mathrm{h}}{4\mathrm{\pi }}\mathrm{\hspace{1em}}\text{ or }\hspace{1em}\mathrm{\Delta x}.\mathrm{\Delta v}\ge \frac{\mathrm{h}}{4\mathrm{\pi m}}$

4. Quantum numbers:

The electron in an atom can be characterised by a set of four quantum numbers, namely principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m) and spin quantum number (s).

5. Electronic configuration:

(i) Aufbau principle : Once the lower energy orbitals are completely filled, then the electrons enter the next higher energy orbitals.

(ii) Pauli exclusion principle : No two electrons in an atom can have the same set of values of all four quantum numbers.

(iii) Hund's rule: It states that electron pairing in the degenerate orbitals does not take place until all the available orbitals contains one electron each.

(iv) Number of subshells in ${\mathrm{n}}^{\mathrm{th}}$ shell $= \mathrm{n}$

(v) Number of orbitals in ${\mathrm{n}}^{\mathrm{th}}$ shell$={\mathrm{n}}^2$

(vi) Number of electrons in ${\mathrm{n}}^{\mathrm{th}}$ shell$=2{\mathrm{n}}^2$

(vii) Number of orbitals in subshell $= 2\mathrm{l} + 1$

(viii) Number of electrons in subshell $= 2(2\mathrm{l} + 1)$

(ix) Total number of nodes in any orbital $= \mathrm{n} - 1$

(x) Number of spherical/radial nodes in any orbital $= \mathrm{n} - \mathrm{l} – 1$ where, $\mathrm{l} =$ number of angular nodes.