Which of the following statements in relation to the hydrogen atom is correct?

The correct option is: 3s, 3p and 3d orbitals all have the same energy

Explanation:

In a hydrogen atom (or any single-electron system like ${\mathrm{He}}^{+}$ or ${\mathrm{Li}}^{2+}$), the energy of an orbital depends solely on the principal quantum number (represented by n).

Unlike multi-electron atoms where electron-electron repulsions cause subshells with different values of the azimuthal quantum number (l) to split in energy, a hydrogen atom experiences no such inter-electronic repulsion. Consequently, all orbitals sharing the same principal quantum number n are degenerate, meaning they possess the exact same energy level.

For the third shell ($n=3$), the available orbitals are the 3s ($l=0$), 3p ($l=1$), and 3d ($l=2$) orbitals. Since they all share the same principal quantum number ($n=3$):

$E_{3s}=E_{3p}=E_{3d}$

Therefore, in a hydrogen atom, the 3s, 3p, and 3d orbitals all have the same energy.