How do I find the Ground State Energy?

Question

So, I need to know the general way to find the ground state energy, but I've provided an example problem so you know what I'm asking.

You have a cold gas of atoms, and you observe that if you shine light consisting of photons with energy 6 eV or greater through the gas, some free electons are observed, implying that photons of such energies are able to ionize an atom in the gas (that is, separate an electron from an atom). You find that with photons of less than 6.0 eV, no ionization occurs.

What is the energy of the ground state? K+U=?

So I really really need to know this for the exam, and I somehow missed it. If anyone could please give an explanation (the answer is -6 eV), I would be very very appreciative. :-D

Answer 1

Simple - 6 eV is required to separate an electron from its atom. When it is ionized, the eelctron has no kinetic energy. That means all of the 6 eV went to raising the electron for its ground state energy to the ionization level.

Ground state energy + 6 eV photon = 0 eV kinetic energy

Thus Ground state energy = - 6 eV

Think of the ionized state as being at zero eV. The ground state has to be at a lower energy level.

Answer 2

You can put the ground state energy at any possible value. It is usually associated with 0 and then the first excited state has a positive energy. But it's really an arbitrary choice since all that matters is the energy difference.

:-)