# Hydrogen Ground State Energies - Question

I am an A-level teacher so I don't want an answer in terms of anything too complicated (for my students!)

The hydrogen atom has a ground state energy of -13.6eV. I am happy with this.

This means that the electron needs 13.6eV of kinetic energy in order to become free of the nucleus.

What I am unsure about is, if the electron has a potential energy of -13.6 eV, then does this mean that it has no kinetic energy? Because if it has kinetic energy, then this would mean that it would need less than 13.6 eV to become free of the nucleus because it already has some of the positive energy it needs.

We teach that the closest the electron can get to the nucleus is when KE=PE. This occurs when r = bohr radius.

So is the actual radius of the ground state electron greater than this so that we can reduce the kinetic energy required so that it has -13.6 eV of energy.

Now of course, I know that we don't know the radius of the electron orbit. We can merely speculate and look at a probability distribution.

I guess what my question could boil down to is: does the ground state electron have an overall energy of 0?

Physics Monkey
Homework Helper
The electron in hydrogren has a binding energy of -13.6 eV. This is the energy it would take to remove the electron from the proton and place it at rest far away. This you know.

This energy cost is not purely potential energy. The potential energy of the electron in the ground state of hydrogen is 2*-13.6 eV = -27.2 eV. The kinetic energy of the electron is + 13.6 eV. The total energy is +13.6 eV - 27.2 eV = -13.6 eV, which is the result you know. The fact that this energy is negative means the electron is bound to the proton, and you must supply energy to liberate it.

The meaning of the binding energy in more detail is as follows. You want to take the electron moving with a kinetic energy of 13.6 eV and with a potential energy of -27.2 eV and move it far away to a final state at rest. Far away means no final potential energy. At rest means no final kinetic energy. You can think of it as putting your initial kinetic energy towards liberating the electron, but even after you use your 13.6 eV of initial kinetic energy, you still need to pay an additional 13.6 eV to get the total energy to zero i.e. an electron at rest far away.

Hope this helps clarify the meaning of the binding energy for your students. I don't know how much you want to get into this, but KE can't equal PE because KE is positive while PE is negative. What is true in hydrogren is that the absolute value of PE is twice KE as I said above.

edguy99
Gold Member
At the bohr radius of hydrogen, about 53 picometers (the size of a hydrogen atom you see in a space filled chemistry picture), it takes 13.6 evolts of energy to remove the electron from the proton using coulombs laws.

It is interesting that the electron never becomes more strongly bound to the hydrogen atom then 13.6 evolts.

To the question "does the ground state electron have an overall energy of 0?"

If you say the electron has -13.6 evolts of KE when bound to the proton then it will take 27.2 evolts worth of energy to free it. If you say the electron has 0 evolts of KE when bound to the proton then it will take 13.6 evolts worth of energy to free it.

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