Confusion on binding energy and ionization energy.

[Cedric Chia]

1) I know that the binding energy is the energy that holds a nucleus together ( which equals to the mass defect E = mc² ). But what does it mean when we are talking about binding energy of an electron ( eg. binding energy = -Z²R/n² ? ). Some website saying that " binding energy = - ionization energy " while the others saying that " binding energy = excitation energy - ionization energy ", which is true and what is the meaning of a binding energy of an electron?

2) What is the relationship between binding energy, ionization energy and excitation energy? ( eg. change in binding energy = change in excitation energy ? )

3) Is the ground state for a multielectron quantum system not necessarily n = 0 ? Let's say Rubidium atom ( atomic number 37 ), what is the quantum number n and L associate to it's ground state and first excitation energy state ? Since it's electron configuration is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s¹ , is the ground state 5s and the first excitation state 4d ( because the next orbital after 5s is 4d ) ?

 

[PeterDonis]

I know that the binding energy is the energy that holds a nucleus together

More precisely, the energy it would take to disassemble the nucleus, i..e, take it apart.

what does it mean when we are talking about binding energy of an electron

The energy it would take to remove the electron from the atom.

Some website saying that " binding energy = - ionization energy " while the others saying that " binding energy = excitation energy - ionization energy "

Can you give specific references?

What is the relationship between binding energy, ionization energy and excitation energy?

I'm not sure what you mean by "excitation energy".

In an atom with one electron (such as a neutral hydrogen atom), the ionization energy and the binding energy are the same thing. For a hydrogen atom in its ground state, that energy is 13.6 eV: it takes 13.6 eV to ionize the atom (remove the electron from it), so that is the binding energy.

In atoms with multiple electrons, it gets more complicated.

Let's say Rubidium atom ( atomic number 37 ), what is the quantum number n and L associate to it's ground state and first excitation energy state ?

There isn't a single n because the atom has more than one electron.

Since it's electron configuration is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s¹ , is the ground state 5s and the first excitation state 4d ( because the next orbital after 5s is 4d ) ?

No. The entire electron configuration is the ground state.

 

[Cedric Chia]

In atoms with multiple electrons, it gets more complicated.

For a single electron system, it's binding energy would just be -RZ²/n² (where R = 13.606(eV) ). But when we're talking about multielectron system, it's binding energy would become -RZ_eff²/n² (since there will be shielding effect due to the inner elecrons, where we need to figure out the Z_eff before finding the value of binding energy of each electrons? )

I'm not sure what you mean by "excitation energy".

Excitation energy is the discrete amount of energy required to promote an electron from ground state to higher energy state ( eg. an excitation energy of 10.2 electron volts is required to promote the electron from its ground state to the first excited state. A different excitation energy (12.1 electron volts) is needed to raise the electron from its ground state to the second excited state ).
Having said that, what is the relationship between excitation energy, binding energy and ionization energy? (eg. binding energy = - ionization energy?, change in binding energy = excitation energy? ).

No. The entire electron configuration is the ground state.

Does it mean that for the outer electron, it's ground state is 5s and for the atom itself the entire electron configuration is it's ground state, since that is the most probable way to have lowest energy state, and the first excited state happen when the outer electron promoted to the next energy level?

 

[PeterDonis]

when we're talking about multielectron system, it's binding energy would become -RZeff2/n2

It's more than that: for a multi-electron system, there are multiple possible "binding energies", so you have to be more specific: are you referring to the energy required to remove the outermost electron from the atom? Or to remove two or three? Many metallic elements have ions with more than one positive charge (meaning with more than one electron removed). Or are you referring to the additional energy required to remove, say, a second electron after one has been removed? All of these energies are different.

Excitation energy is the discrete amount of energy required to promote an electron from ground state to higher energy state

Ok.

Having said that, what is the relationship between excitation energy, binding energy and ionization energy?

There isn't one. Excitation energy is just a different thing: promoting an electron from ground state to a higher energy state is just a different thing from removing it from the atom altogether. There is no necessary relationship between the energies involved.

Does it mean that for the outer electron, it's ground state is 5s

No. The atom as a whole has a ground state, not individual electrons. You can say that when the atom is in its ground state, the electron configuration is what you gave.

for the atom itself the entire electron configuration is it's ground state, since that is the most probable way to have lowest energy state

It's not the "most probable way" to have the lowest energy state; it is the lowest energy state (the only one).

the first excited state happen when the outer electron promoted to the next energy level?

That's one way of having an excited state, but not the only one. You could also promote some other electron besides the outermost one.