Energy Levels
How do we explain the fact that atoms of a certain element emit light with definite wavelengths when their atoms are excited?
Consider a hydrogen atom, which is just an electron in orbit around a proton, as simple as you can get.
| The electron has kinetic energy but not enough to escape the attraction of the proton | We can think of it as being trapped in a "potential well".
The electron however, cannot have any amount of energy. |
The electron can only have certain amounts of energy. Our well is stepped. We will see why later. |
The atom has definite energy levels. The lowest amount of energy is the ground state ( n = 1 ) and there are definite levels above this. To get to a higher level the electron would need to gain energy, perhaps by absorbing a photon. The electron would then fall to a lower energy by emitting a photon.
Because the energy levels are fixed the atom can only absorb photons which have a certain amount of energy, i.e. have a certain wavelength.
So this explains why all hydrogen atoms emit photons of the same wavelength. Because all hydrogen atoms have the same fixed energy levels.
The energy levels get closer together as they get higher.
If an electron gets to n = infinity then it has escaped.
The difference in energy between n = 1 and n = infinity is equal to the ionisation energy of hydrogen.
The levels are often said to correspond to a negative amount of energy, after all if the electron has escaped then it has zero potential energy.
So is there a pattern to these levels or are they random? There is a pattern and it is surprisingly simple.
The ionisation energy of hydrogen is 13.6 eV so we say that the ground state corresponds to an energy of -13.6 eV
| n | energy (eV) | n2 | 13.6 / n2 |
| 1 | -13.6 | 1 | 13.6 |
| 2 | -3.4 | 2 | 3.4 |
| 3 | -1.5 | 3 | 1.5 |
| 4 | -0.85 | 4 | 0.85 |
It appears that we can calculate energy levels using the equation E = (-13.6 eV) / n2 where n is an integer.
The situation for elements other than hydrogen is more complicated because there are a number of electrons and their energy levels effect each other. Nevertheless it is amazing to find such a simple elegant pattern for something, atomic spectra, which appeared so random.
Why does this pattern exist? The PowerPoint "The Music of Atoms" should help to explain that question.