Ionization energy and energy levels

[ilovepudding]

TL;DR Summary

Is ionization energy equal to the required energy to remove the valence electron or to remove one of the two electrons in the K shell?

Hi,
The ionization energy is defined as the minimum amount of energy required to remove the most loosely bound electron, the valence electron, of an isolated neutral gaseous atom.

Our physics teacher also told us while explaining this concept in the context of energy levels, that it is equal to the energy of the ground state, that is the closest shell to the nucleus.

Now, he explained that using a hydrogen atom so I kinda got the point. But how about a lithium atom? Is ionization energy equal to the required energy to remove the valence electron or to remove one of the two electrons in the K shell?

I think I am missing something here, but I don't know what exactly. HELP.

 

[nrqed]

Summary:: Is ionization energy equal to the required energy to remove the valence electron or to remove one of the two electrons in the K shell?

Hi,
The ionization energy is defined as the minimum amount of energy required to remove the most loosely bound electron, the valence electron, of an isolated neutral gaseous atom.

Our physics teacher also told us while explaining this concept in the context of energy levels, that it is equal to the energy of the ground state, that is the closest shell to the nucleus.

Now, he explained that using a hydrogen atom so I kinda got the point. But how about a lithium atom? Is ionization energy equal to the required energy to remove the valence electron or to remove one of the two electrons in the K shell?

I think I am missing something here, but I don't know what exactly. HELP.

It is the energy required to remove one electron (the most loosely bound) from the neutral atom (it can be also applied to molecules but let's stick with atoms). Hydrogen is not a useful example to explain ionization energy in general, I agree.

See for example http://hyperphysics.phy-astr.gsu.edu/hbase/Chemical/ionize.html

 

[PeterDonis]

Our physics teacher also told us while explaining this concept in the context of energy levels, that it is equal to the energy of the ground state, that is the closest shell to the nucleus.

This doesn't make sense. The ionization energy can be thought of as the difference in energy between the ground state of the neutral atom and the single ionized state (where one electron is free and the remaining ones are still in the energy levels they were in before). But that's not the same as the energy of the ground state, or the energy of an electron in the closest shell to the nucleus.

 

[ilovepudding]

If the ionization energy is the difference between the the ground state of the neutral atom and the single ionized state, it should allow the electron in the closest shell to the nucleus to jump all the way out of the atom and become a free electron right? We shouldn't be talking about the valence electron anymore, because the valence electron would require a tiny bit of energy compared to that difference between the ground state of the neutral atom and the single ionized state.

 

[nrqed]

This doesn't make sense. The ionization energy can be thought of as the difference in energy between the ground state of the neutral atom and the single ionized state (where one electron is free and the remaining ones are still in the energy levels they were in before). But that's not the same as the energy of the ground state, or the energy of an electron in the closest shell to the nucleus.

True but in the case of hydrogen, the ionization energy is minus the energy of the state. They are not equal but they differ only in sign so I can see why someone could cut corners and say that they are "equal" (really meaning that the ionization energy is the absolute value).

 

[PeterDonis]

If the ionization energy is the difference between the the ground state of the neutral atom and the single ionized state, it should allow the electron in the closest shell to the nucleus to jump all the way out of the atom and become a free electron right?

Not unless the atom is hydrogen (or helium, strictly speaking, which also has electrons in only one shell in its ground state).

In any other atom, the electron that is getting removed when going to the singly ionized state is not the electron in the lowest shell.

We shouldn't be talking about the valence electron anymore, because the valence electron would require a tiny bit of energy compared to that difference between the ground state of the neutral atom and the single ionized state.

You appear to misunderstand what "singly ionized state" means. It means the state in which the valence electron--or more precisely one of the electrons in the outermost shell, since not all atoms have just one and not all of those electrons are valence electrons (think of noble gases)--is removed. In other words, it's the state in which one of the electrons that takes the least energy to remove from the atom, is removed. That least energy is the ionization energy.

 

[PeterDonis]

in the case of hydrogen, the ionization energy is minus the energy of the state

That depends on how you define the zero of energy. I agree that the definition of the zero as the energy of the state in which no particles are bound is common, and by that definition, for hydrogen only, the ionization energy is minus the energy of the ground state. But since that is only true for that one special case and for that one choice of the energy zero point, it doesn't seem very useful to me as a pedagogical guide.

 

[nrqed]

If the ionization energy is the difference between the the ground state of the neutral atom and the single ionized state, it should allow the electron in the closest shell to the nucleus to jump all the way out of the atom and become a free electron right? We shouldn't be talking about the valence electron anymore, because the valence electron would require a tiny bit of energy compared to that difference between the ground state of the neutral atom and the single ionized state.

The ionization energy is defined as the energy required to remove the least bound electron. So it is not an electron in the closes shell unless you are dealing with Hydrogen or Helium.
It does not necessarily take a tiny bit of energy! Look at the graph I linked to in my previous post. In atoms with filled shells, it takes a lot of energy to remove an electron even in the outer shells. In alkali atoms, when the lest bound electron is alone in a shell, it does take much less energy indeed.

 

[ilovepudding]

so what this is saying is that, in general, the ground state is not necessarily the lowest shell, right? It's the state in which the electrons of the valence shell are as low as they can possibly be, correct me if i am wrong.

 

[PeterDonis]

so what this is saying is that, in general, the ground state is not necessarily the lowest shell, right?

No. You seem to misunderstand what "ground state" means. "Ground state" means that it is not possible for any electron in the atom to move to a lower energy shell than it is currently in. It is a state of the atom as a whole; it is not a state of any particular energy shell.

It's the state in which the electrons of the valence shell are as low as they can possibly be

This is true of all the electrons in the ground state, not just the electrons of the valence shell.

 

[ilovepudding]

Okay, thanks for the clarification, I understand now.

 

[nrqed]

That depends on how you define the zero of energy. I agree that the definition of the zero as the energy of the state in which no particles are bound is common, and by that definition, for hydrogen only, the ionization energy is minus the energy of the ground state. But since that is only true for that one special case and for that one choice of the energy zero point, it doesn't seem very useful to me as a pedagogical guide.

I agree completely, which is why I kept emphasizing it when my comments applied to hydrogen only. This is also why in post 2 I mentioned that hydrogen was not a good example to focus on for this topic since it can be misleading.

Cheers!