What Happens to an Electron When it is Excited and Removed from an Atom?

[UchihaClan13]

Okay guys
Felt a need to post this since it's been confusing me for a long time
Say,for example,we have an atom with its electron occupying the 3s orbital
Now let's say we energise the atom and constantly supply it energy that the electron which receives the energy(or a part of it)gets excited and goes to an excited state
Now let's say this energy supply is kept constant
Hence there would be a time when the electron is "removed"/isolated from the atom
But as we all know
Orbitals are just

 

[UchihaClan13]

I'll write the rest of the post later

 

[UchihaClan13]

Something happened with the post i made

 

[UchihaClan13]

Okay
So orbitals are just one-electron spatial wave functions which have their existence when the coordinates of an electron/position of an electron at a particular time need to be defined
Now
Let's say we energise an atom
As a consequence of this,the electron(WLOG, i assume any valence electron) also gets excited and goes to an excited state
Now let's suppose that the energy supply to the atom is kept constant(energy is being supplied at a constant rate)
Due to this,the kinetic energy of the atom and the energy of the electrons will increase(I neglect doppler broadening and the direction from which you supply the beam of photons)
Now my question is:
Since we know an atom consists of an infinite number of orbitals(orbitals exist/have their meaning only when an electron occupies them or when a particular wavefunction of the electron defines its properties in its energised state)
Let's say when an electron in the 3s orbital of sodium is excited ,it enters the 3p orbital because its energy has increased and the 3p orbital is the wavefunction which describes its properties now
So since an atom consists of infinite orbitals(which are present in a virtual manner/state,so to speak),how can we decide the last orbital which the electron occupies??Do we just find the sum of the total energy(kinetic and potential energy) of the electron and if it's zero(which means it's no longer under the influence of the attractive electrostatic force provided by the nucleus),we conclude it has been "removed" from the atom and the energy required to remove it is thus defined as the ionisation energy.
Another method which can be employed to check the "removal" of an electron from an atom is to measure the electron cloud densities after supplying large amounts of energy to the atom.If there's any sort of fluctuation,it can be concluded that the electron has been thus "removed"from the atom

But can't we provide an explanation which is based on quantum mechanics or employs a similar type of analogy?
Or is it just something which happens and can't be defined?

Some insight and help is much appreciated!:)UchihaClan13

 

[CrazyNinja]

Theoretically speaking, the electron is never free from the nucleus (for simplicity let's consider Bohr's model). So the electron is never completely removed from the atom.
However in this case, the sum of energies = 0 works, because we have only this atom and nothing else in the universe (Bohr's model). Thus all other interactions can be ignored.

For multi-electron systems, the case becomes complex. And if the atom is not isolated, then there are more and more complex situations. These I cannot answer, for I do not know enough.

 

[Borek]

While there are infinitely many orbitals, their energies don't end at infinity.

Imagine you have a number sequence $a_k = 1 - \frac 1 {2^k}, k \ge 1$. This sequence contains infinitely many numbers that are lower than 1, we can't say which is the last one (there is no last one), yet we can be perfectly sure any number x > 1 is not a member of the sequence. Now treat these numbers as "energies" and you have a nice analogy of the orbitals - the "energy" on the first one is ½, there is no last one, yet we know that if we add more energy than ½ the electron will be no longer combined with the atom.

 

[DrDu]

While an atom has an infinite number of discrete bound states, it also has a continuum of non-bound states corresponding to one or several electrons and an ion. These states are also called scattering states and there are whole books dedicated to their quantum mechanical description. What happens to an atom when you bring it into the field of - say - a laser depends on both the intensity and the frequency of the latter. If the intensity is weak, the laser will only excite the atom if it's energy corresponds to the difference of energy of some energy levels and if there is a non-vanishing transition dipole moment between these levels. However the laser may not only excite the atom but can also de-excite it again. This may give rise to a coherent dynamics which is called Rabi-oscillations. If the field is strong, the laser can induce much more complex transitions and also ionize the atom due to multiphoton absorption.

 

[UchihaClan13]

Theoretically speaking, the electron is never free from the nucleus (for simplicity let's consider Bohr's model). So the electron is never completely removed from the atom.
However in this case, the sum of energies = 0 works, because we have only this atom and nothing else in the universe (Bohr's model). Thus all other interactions can be ignored.

For multi-electron systems, the case becomes complex. And if the atom is not isolated, then there are more and more complex situations. These I cannot answer, for I do not know enough.

exactly that's what i thought

While there are infinitely many orbitals, their energies don't end at infinity.

Imagine you have a number sequence ak=1−12k,k≥1ak=1−12k,k≥1a_k = 1 - \frac 1 {2^k}, k \ge 1. This sequence contains infinitely many numbers that are lower than 1, we can't say which is the last one (there is no last one), yet we can be perfectly sure any number x > 1 is not a member of the sequence. Now treat these numbers as "energies" and you have a nice analogy of the orbitals - the "energy" on the first one is ½, there is no last one, yet we know that if we add more energy than ½ the electron will be no longer combined with the atom.

So what you're implying is that if the electron's energy is greater than 1,it does not remain as a member of the atom which follows "the quantization"rule
And thus we assume /conclude it has separated from the atom

Right?
Could you explain me the same thing for multi-electron systems?UchihaClan13

 

[Borek]

And thus we assume /conclude it has separated from the atom

Yes.

For a multielectron atom it is very similar behavior in general. The most important difference is that once one electron is removed, removing next electron becomes more difficult (so the maximum possible energy becomes higher). The sequence of energies becomes different as well, but there are still infinitely many below some maximum level.

 

[UchihaClan13]

Can the energies of the excited electrons be measured
And here for hydrogenic species
Isn't the quantization of energy the same as the variation integral which is approximated/guessed to be equal to the ground state energy(E_I)
And the basis of quantization is the trial function which is the combination of a constant c*the wavefunction of the electron

Basically the permissible values of energy which can be taken by the electron for hydrogenic species is Hψ=Eψ where H is the hamiltonian operator
Right?
For multi-electron systems we use the variation/perturbation theories
and SCF-MO treatments right??(Such as the hartree-fock method)
When the energy of any electron cannot be defined by these relations or does not correspond with these patterns,we claim that the electron is no longer under the influence of the atom and has been "removed"
Right?
UchihaClan13

 

[UchihaClan13]

so the maximum possible energy becomes higher)

Maximum possible energy?
Do you mean the maximum energy that an electron could possesses in a certain orbital has increased?
If yes,then yes it should considering the nuclear attraction/interaction(net) on each electron has increased and the energy that would be required to make one of them gain enough maximum energy and not follow the "quantization"rule will also obviously increase
Right?UchihaClan13

 

[Borek]

I mean maximum possible energy of an electron that is still part of the atom.

Energy is always quantized, just the sequence of possible energies is not always the same, as it depends on several factors.