Ionization energy of electrons?

[kraphysics]

I am in grade 12 physics and we're currently doing atomic physics. So far I understand that when electrons get excited, they move on to higher energy levels by absorbing photons. Also I understand that when an electron moves from a higher energy level to a lower one, photons are emitted. But my textbook mentions that the ionization energy of helium is simply the energy of the first energy level, En 1 = -2.18 * 10^-18. I dont understand why the ionization energy is En 1? Could someone explain? Thanks

This is not a homework question. I am just curious.

[Bill_K]

Sure, it's because when you ionize the atom, one of the electrons has to go all the way from the ground state where it was, out to infinity. In the ground state it has energy En 1, and at infinity it has energy zero (by definition). So the difference is En 1.

[kraphysics]

Sure, it's because when you ionize the atom, one of the electrons has to go all the way from the ground state where it was, out to infinity. In the ground state it has energy En 1, and at infinity it has energy zero (by definition). So the difference is En 1.

Thank you. But I always thought that the outermost electrons are lost when an atom is ionized, not the ones in n = 1.

[alxm]

Thank you. But I always thought that the outermost electrons are lost when an atom is ionized, not the ones in n = 1.

It requires the least energy to ionize the outermost electrons, but if they absorb an energetic enough photon (gamma-ray) then you can ionize from the innermost orbitals as well.
That's then followed by a photon being emitted as another electron moves down to fill the 'hole', this is called the Auger effect (http://en.wikipedia.org/wiki/Auger_effect).

So regardless of which electron gets kicked out, after a few instants it'll be as if you'd removed one of the outermost electrons anyway, since that's the lowest-energy state for the ion.

[kraphysics]

It requires the least energy to ionize the outermost electrons, but if they absorb an energetic enough photon (gamma-ray) then you can ionize from the innermost orbitals as well.
That's then followed by a photon being emitted as another electron moves down to fill the 'hole', this is called the Auger effect (http://en.wikipedia.org/wiki/Auger_effect).

So regardless of which electron gets kicked out, after a few instants it'll be as if you'd removed one of the outermost electrons anyway, since that's the lowest-energy state for the ion.

Sorry. I am having trouble following. Originally the question was why is the ionization energy of Helium the energy of its 1st energy level?
E 1= -2.18 * 10^18 J
General formula for energy is, En = -E1 / n^2
So to ionize it would be the change in E between final state and initial state, right? So that means that the electrons in the first orbital are brought out to infinity orbital?
Is what I'm saying correct?

[alxm]

Sorry. I am having trouble following. Originally the question was why is the ionization energy of Helium the energy of its 1st energy level?
E 1= -2.18 * 10^18 J
General formula for energy is, En = -E1 / n^2
So to ionize it would be the change in E between final state and initial state, right? So that means that the electrons in the first orbital are brought out to infinity orbital?
Is what I'm saying correct?

Hydrogen, not helium (since hydrogen only has one electron).

Anyway, the way this works is that we define the zero energy level for the electron as the situation where it's infinitely far away from the nucleus, and stationary. In other words, no kinetic energy (relative the nucleus) and no potential energy (since it's infinitely far away from the nuclear attraction).

So in the orbitals (bound states) the energy of the electron is negative, because it's closer to the nucleus. So the ground state is the state where the electron has the lowest, most negative, energy. Lower than zero energy means the electron is bound - it has less energy than required to escape the attraction of the nucleus. But the electron can also have more than zero energy. Because once the electron is free of the nuclear attraction it no longer has quanized energy levels, it can move freely. And so it can have any energy then. So above zero you don't have orbitals or any discrete states, but a continuum of energy levels.

So the ionization energy isn't defined as the difference between the final and initial states, because the final state could have the electron flying away at any arbitrary speed. So instead it's defined as the minimum energy required to remove the electron from the atom. Which means, the difference between zero, and the energy of the orbital the electron is in.

So since the ground-state energy of the one electron in hydrogen is -2.18 * 10^18 J, it has an ionization energy of that amount (without the minus sign). But you can still ionize the atom with any amount of energy that's greater than that.

[kraphysics]

I think I understand. :smile: Thanks a lot!