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Discrete Energy Levels

Physics: IB Diploma Higher Level, topic 5.1.4

Energy Levels in Atoms

Electrons in atoms must occupy a discrete energy level.

Energy levels

Energy levels

  • Electrons do not float around randomly in atoms.
  • They can only be found at set energy levels.
  • Each energy level is given a 'quantum number'.
  • The ground state is the lowest energy level. The ground state has n = 1.
  • The higher the energy level, the larger its quantum number, n.
Transitions between energy levels

Transitions between energy levels

  • An electron can transition between energy levels by absorbing or emitting a photon of a specific frequency.
  • If an electron emits a photon, it will drop in energy level.
  • If an electron absorbs a photon, it will rise to a higher level.
  • In both cases, the photon must have energy exactly equal to the energy difference between the levels.
Equation

Equation

  • The movement of electrons between energy levels can be represented in the equation:
  • ΔE=E1−E2=hf=hcλ\Delta E = E_1 - E_2 = hf = \frac{hc}{\lambda}
  • This shows that the energy difference between levels one and two is equal to the energy of the emitted (or absorbed) photon.
Excitation and ionization

Excitation and ionization

  • If an electron absorbs a photon and jumps up an energy level, we say it has been excited.
  • If an electron absorbs a photon that is so energetic it is knocked out of the atom altogether, the electron has been ionized.

Ionization and Excitation

Both electrons being removed from an atom and the movement of electrons within energy levels in the atom explain commonly observed phenomena.

Ionization

Ionization

  • To ionize an atom means to remove or add electrons to an atom.
  • Ionization in the context of quantum phenomena almost always means the removal of electrons completely from the atom.
  • The energy needed for an electron to go from the ground state to be completely removed is called the ionization energy.
Excitation

Excitation

  • Electrons can also be made to move from one energy level to the other.
  • To do this, the electron needs exactly the energy difference between energy levels.
  • One way to do this is for a photon to interact with the electron.
  • The electron will absorb all the energy of the photon.
Excitation 2

Excitation 2

  • If the energy of the photon is exactly the energy difference between the energy levels, the electron will move up the energy levels.
  • When an electron has moved up energy levels we called the electron "excited".
  • The process of making the electron move up energy levels is called "excitation".

Test yourself on Discrete Energy Levels

  • What is the quantum number for the ground state of an electron?

  • What is the correct equation for the change in energy between energy levels?

  • When will an electron move into a higher energy level?

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