Energy Levels and Photon Emission

Energy Levels in Atoms

Atoms can interact with photons of lower energy than is required to remove electrons from them.  The photons we looked at in the photoelectric effect could remove the electrons from very reactive metals like caesium.  Photons can interact with other atoms to give them extra energy, which makes them excited.

When we heat a gas or pass an electric current through it we can make it glow.  We have ionised the gas.  If we look at the glowing gas through a spectrometer, we see the spectrum of the gas which is distinctive for that gas.  Unlike the spectrum of the Sun, in which we see all the colours of the rainbow, we only see certain colours, while others are absent.  We call this kind of spectrum a line emission spectrum.  The colours are discrete wavelengths

When a gas is ionised, one or more outer electrons are ripped off.  The molecule has become positive.  It will recombine with an electron and lose energy, giving that energy in the form of a photon.  Other atoms may not have been ionised, but are still in a very excited state.  The atoms have interacted with the photon and the electrons have moved to a higher energy level.

About a microsecond later, the electrons lose their energy as a photon and return to the stable state, called the ground state.  The important thing to remember is that electrons can only exist at permitted energy levels.   It’s like a person standing on a ladder; he can exist at one rung up, two rungs, etc., but NOT at a height of 1.5 rungs.  We call the idea of the energy ladder quantum theory.

As we consider energy levels in atoms, we will look at hydrogen which fits this model well.  (Hydrogen has one electron.)  More complex atoms with several electrons do not.

If we look at a spectrum of hydrogen, we find lines at several discrete wavelengths.

The electron does a job of work in releasing a photon; it has lost potential energy.  Therefore we start at the highest level which we give a value of zero.  Therefore the electron falls from the zero point to the –3.41 eV level.  The more negative the level, the lower the energy level.

The highest energy level is where ionisation occurs.  The lowest level is the ground state.

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.  This 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

Let's have a look at a worked example: