Question

Question #91ae7

Answer 1

Well, the Bohr model ONLY works for the hydrogen atom, so this is only useful for the hydrogen atom... or atoms with one electron (which are not that useful).

For multi-electron atoms, we must account for electron correlation, which splits the orbitals by their angular momentum (e.g. `3s, 3p, 3d`, not just "`3`").

Clearly, a given `n` will have multiple energy sublevels (`s,p,d,f,g, ...`), and it is insufficient to only have one quantum number `n` to describe the energies.

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We know the Rydberg equation

`DeltaE = E_(n_f) - E_(n_i) = -"13.6 eV"(1/n_f^2 - 1/n_i^2)`,

which is really just using initial and final states `E_(n_i)` and `E_(n_f)` for an electron's energy transition in the hydrogen atom from initial to final principal quantum number, `n_i` to `n_f`.

So, taking only one of these states gives

`bb(E_n = -(13.6 "eV")/(n^2))`

for the energy level for the principal quantum number `n` in the HYDROGEN atom.

You can see this work for the hydrogen atom.

`E_2 = -"13.6 eV"/(2^2) = -"3.4 eV"`

`E_3 = -"13.6 eV"/(3^2) = -"1.51 eV" ~~ -"1.5 eV"`

`E_4 = -"13.6 eV"/(4^2) = -"0.85 eV" ~~ -"0.9 eV"`

etc.