Question

Can an electron transition from a `3p` to a `4f` orbital? For example say an atom has `3s^2 3p^8 4f^5`?

Answer 1

No, not in one step... especially because that is not a real atom!

A `3p -> 3d -> 4f` two-step transition is allowed. A `3p -> 4f` one-step transition is not allowed because it is forbidden by symmetry as per Laporte selection rules.

A real-life example is when sulfur undergoes the following transitions:

`3s^2 3p^color(red)(4) -> 3s^2 3p^color(red)(3) 3d^color(red)(1)` `" "" "`(`""^3 P -> ""^3 D`, about `"70165 cm"^(-1)` upwards)

`3s^2 3p^color(red)(3) 3d^color(red)(1) -> 3s^2 3p^color(red)(3) 4f^color(red)(1)` `" "`(`""^3 D -> ""^3 F`, about `"6490 cm"^(-1)` upwards)

or in short, `3p -> 3d -> 4f`.

The first transition would require input of `"8.70 eV"` of energy (about `64%` the ionization energy of hydrogen atom), and the second would require about `"0.805 eV"` of energy.

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For one, `p` orbitals on one energy level can only have `bb6` electrons in them... not `8`. Also, there must be `bb(3d)` orbitals in between `3p` and `4f`. The `3d` orbitals exist starting at `n = 3`, and you cannot skip over them!

The total orbital angular momentum can only change in steps of `1` at a time, as per the spectroscopic selection rules.

`DeltaL = pm1` `->` due to symmetry rules as stated above

`DeltaS = 0` `->` electron spin is odd parity, so spin flips are forbidden if orbital parity change is to be enforced

where:

• `L = |sum_i m_l(i)|` is the total orbital angular momentum for summing the `m_l` values for the `i`th electron in each orbital of a given `l`.
• `S = |sum_i m_s(i)|` is the total spin angular momentum for summing the `m_s` values for the `i`th electron in each orbital of a given `l`.

In more explicit terms...

• With `DeltaL = pm1`, we mean that the wave function parity must change between even and odd for transitions, i.e. the `l` of the starting orbital can only be different from the `l` of the destination orbital by `1`:

`s = "even symmetry"`
`p = "odd symmetry"`
`d = "even symmetry"`
`f = "odd symmetry"`

So you can only have `3p -> 3d` let's say, and then `3d -> 4f`. You cannot have `3p -> 4f` directly in one step.

• It is also known that `DeltaS = 0`, meaning the total spin cannot change (otherwise the new spin parity would change the total parity to be the same as before).

So, you can't (easily) go from `ul(uarr darr)` to `ul(uarr (darr)` by promoting one of those electrons to a higher energy level.