Quantum Physics Tutorial 4 - Energy Levels in Atoms

We have seen that:

The electron does a job of work in releasing a photon. It loses potential energy.
The highest energy level is where ionisation occurs. The lowest level is the ground state.
Ionised atoms give out light as the electrons fall back to the ground state.
Photons of sufficient energy can cause ionisation. This is how gamma rays interact with atoms to ionise them.

In excitation, a photon or electron interacts with an electron in the electron shells. The electron is raised to a higher energy level, but is NOT removed. It rises to a higher energy level. Almost immediately it falls back to the ground level, emitting photons. However it has to be exactly the right energy. The picture shows two energy levels in an imaginary atom.

Note that the values here are shown as positive, the ground state being zero. This has been done for simplicity. The ionisation energy of this atom is a lot more than 6.4 eV.

The in-coming photon has to be exactly 6.4 eV. There are three possible energies for emitted photons:

6.4 eV, if the electron falls straight back to the ground state;
4.8 eV, if the electron falls from the 4.8 eV level to 0 eV;
1.6 eV if the electron falls from the 6.4 eV to the 4.8 eV level.

If the photon is 6.35 eV, it will not be absorbed. It has to be 6.4 eV.

Electrons can make transitions from any energy level to any other:

These transitions give us photons in the visible spectrum. In fact, the ground state is at –13.6 eV. So transitions to the ground state will give photons in the UV region.

The transition from -13.6 eV to 0 eV is the ionisation energy of hydrogen, the energy required to strip an electron from the atom.

We need to be aware of the following points:

The lowest level (-13.6 eV) is the ground state. This is the normal configuration of the atom. Energy must be put in to raise the electron to other levels.

The highest level is the ionisation energy.

Energy levels are not evenly spaced.

We can quantify this in an equation. If an electron is at an excited level (E₁) and makes a transition to a lower level (E₂), then the energy of the photon given out can be worked out with the equation:

E = E₁ – E₂

Since E = hf, we can rewrite this as:

hf = E₁ – E₂

Question 1	(a) An excited atom loses its energy quickly. How does it do this? (b) What is the frequency of a photon given out by a transition from -0.85 eV to -1.51 eV?
Question 2	Hydrogen has an ionisation energy of 13.6 eV. Explain what would happen if a hydrogen atom interacted with: a. An electron of energy 22.1 eV; b. A photon of energy 13.6 eV; c. A photon of energy 6.1 eV.

When photons are absorbed, all their energy is used to raise the electron to the higher energy level. Immediately, the electron falls to the ground state, photons are emitted. The frequency (or wavelength or colour) depend on the transitions. Remember that all transitions will be seen, as there are thousands of millions of atoms. The photons are retransmitted in all directions.

If we burn sodium compounds (e.g. sodium chloride) in a bunsen flame, we see an orange flame. If we shine a sodium lamp onto the flame, we see a dark shadow on a screen.

The photons given out by the sodium atoms are the same wavelength as the light given out by the sodium lamp. As the photons from the flame are transmitted in all directions, the photon intensity on the screen produced by the flame is nowhere near that on the rest of the screen. Therefore we see a shadow. This is the principle used in absorption spectra.