Final answer:
In hydrogen, the 3s, 3p, and 3d orbitals have the same energy due to the presence of only one electron, making their energies depend on the principal quantum number. In many-electron atoms, the differences in shielding and penetration of the subshells remove the degeneracy, resulting in different energies for these orbitals.
Step-by-step explanation:
The 3s, 3p, and 3d orbitals have the same energy in a hydrogen atom because hydrogen has only one electron, and the energy levels are solely dependent on the principal quantum number n. In a hydrogen atom, orbitals with the same value of n are degenerate, meaning they have the same energy. However, in a multi-electron atom, these orbitals have different energies due to electron-electron interactions that remove the degeneracy. Electrons in different orbitals shield each other from the full charge of the nucleus, which means that, for example, 3p electrons will be shielded by the 3s electrons. This shielding effect contributes to differences in energy between subshells within the same principal energy level. Additionally, as quantum mechanics predicts more than one orbital with different electron density distributions within each principal shell, the different subshells, characterized by different angular momentum quantum numbers l, have different penetration and are affected differently by the nuclear charge, and hence, they acquire different energies in a many-electron atom.