Final answer:
In one-electron systems like hydrogen atoms, orbitals with the same principal quantum number have identical energy levels due to the absence of electron-electron interactions that would otherwise differentiate them. This state is called degeneracy, and the energy depends solely on the principal quantum number, not the angular momentum quantum number.
Step-by-step explanation:
In one-electron systems such as a hydrogen atom, all orbitals with the same principal quantum number (n) have the same energy levels, and this condition is known as degeneracy.
The energy of an orbital in a one-electron system is determined only by the principal quantum number (n), and the angular momentum quantum number (l) does not affect it. This is because there is no electron-electron repulsion that can cause variations in energy levels.
The energy levels in such systems increase smoothly as the principal quantum number (n) increases, which is expressed as En & 1/n². In atoms with more than one electron, this degeneracy is lifted due to electron-electron interactions, leading to different energy levels for orbitals belonging to different subshells (e.g., 2s versus 2p).
Furthermore, according to quantum mechanics, the energy levels for different values of l (s, p, d, f) within a given principal shell are not significant for understanding spectra of the hydrogen atom under most conditions because there are no interactions among multiple electrons to differentiate them.
The quantum mechanical model predicts a set of orbitals with 4, 9, and 16 different electron density distributions for the n=2, n=3, and n=4 principal shells respectively, as opposed to Bohr's model which allowed only one orbit for each energy level.