Quantum Physics Tutorial 4 - Energy Levels in Atoms

 Contents

Key Words

You will come across these key words in the bold type:

• Electrons make a transition from a higher energy level to a lower.

• Photons are given out that have the same energy as the transition energy.

• The highest energy level is where ionisation occurs.

• The lowest level is the ground state.

Excited atoms

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.

We will consider a hydrogen atom being excited by photons.  Hydrogen is the simplest atom.  Consider a photon being absorbed by a hydrogen atom.  The energy is not enough to ionise the atom, but is sufficient to raise the atom to a higher energy level.  Here the photon is about to interact with the electron:

Remember that a photon is pure energy.  It has to be exactly the right energy.  All the energy is passed to the electron.  It rises to a higher energy level:

Almost immediately, the electron falls back to its original level which is called the ground state.  The energy is emitted as a photon.  The photon travels off in any direction, not necessarily the direction it came from.

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.

Energy Levels in Atoms

Almost immediately the excited electron falls back to the ground level, emitting photons.   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.

In the example above positive values are given.  In most exam questions the following convention is observed:

• The ionisation energy is regarded as 0 eV;

• All other energy levels are negative;

• The most negative energy level is the ground state.  In hydrogen, the ground state is -13.6 eV.

 Read the question carefully to see if the energy levels are in eV or J.  They will show an axis labelled, Energy / eV or Energy / × 10-19 J Before using any equation, such as E = hf, values in electron volt (eV) must be changed to joule (J)

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

# 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 DE of the photon given out can be worked out with the equation:

DE = E1 – E2

The strange looking symbol D is Delta, a Greek capital letter 'D'.  It is physics code for 'change in' or 'difference in'.

Since DE = hf, we can rewrite this as:

hf = E1 – E2

 (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?  Give your answer an an appropriate number of significant figures. 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. Show that a photon emitted in the transition from -3.41 eV to the ground state in hydrogen is in the UV region.

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.

 Ionisation of gases and energy levels in atoms have NOTHING whatever to do with the photo-electric effect.

What is the difference between ionisation and excitation?

 Ionisation Excitation In ionisation, the electron is removed from the atom. In excitation the electron is not removed, but is raised to a higher energy level As long as the colliding electron has more energy than the ionisation energy the electron will be removed. The photon or electron causing the excitation has to have exactly the right amount of energy, else no effect is observed.