Radial wave function depends on n and $\mathcal{l}$ but not on m. Thus each of the three p-orbitals have the same radial form. The wave functions may have positive or negative regions but their radial probability distributions (figure below) show the following features.

• Radial distributions may have several peaks, the number being equal to (n — 1).
• The outermost peak is by far the largest, showing where the electron is most likely to be found. The distance of this peak from the nucleus is a measure of the radius of the orbital and is roughly proportional to n? (although it slightly depends on $\mathcal{l}$ also)

Radial distributions determine the energy of an electron in an atom. The subsidiary maxima at smaller distances are not significant in hydrogen, but are useful in understanding the energies in many electron atoms.

The energies of atomic orbitals in hydrogen atom are given by the formula ${\mathrm{E}}_{\mathrm{n}}=-\frac{\mathrm{R}}{{\mathrm{n}}^2}$

This shows that the energy depends only on the principal quantum number, n. All orbitals with finite n represent bound electrons with lower energy. Energies of individual atoms or molecules are expressed in electron volts (eV) equal to about $1.602\times {10}^{-19}\mathrm{J}$

For many electron atoms

The orbital sizes and energies depend on the atomic number ‘Z

$\text{ Average radius of an orbital }\simeq \frac{{\mathrm{n}}^2{\mathrm{a}}_0}{\mathrm{Z}}$

Where a₀ = Bohr’s radius (59 pm) 1.¢., radius of 1s orbital of hydrogen atom

$\text{ Also }{\mathrm{E}}_{\mathrm{n}}=-\frac{{\mathrm{Z}}^2\mathrm{R}}{{\mathrm{n}}^2}$