Quantum Physics: Energy Levels and Line Spectra

A brief introduction to a topic that students often find tricky.

 

In the planetary or Rutherford model of the atom, negatively-charged electrons orbit the positive nucleus like planets in a solar system. However, under this model electrons should lose energy and spiral into the nucleus.

 

In the Bohr model of the atom, electrons are confined to discrete orbits, representing specific allowed energy levels.

 

The lowest available energy level is called the GROUND STATE. Higher energy levels are EXCITED STATES. Both electrons or whole atoms can be described as excited or in their ground state. An atom with one or more excited electrons is said to be excited. An atom where all the electrons are at their lowest possible energy level is said to be in its ground state.

 

Electron energies tend to be measured in electron-volts (1eV = 1.6 x 10-19 J). The highest energy level for an atomic electron is 0eV – ionisation where the electron breaks free from the atom. All atomic energy levels have negative energies.

 

Electrons can gain energy to move up one or more energy levels (EXCITATION) Electrons in higher energy levels will drop to lower energy levels if a space is available (DE-EXCITATION)

 

Excitation takes place one of two ways: by absorption or collision:

  • Absorption: an atomic electron absorbs a photon and ascends to a higher energy level (excited state). Atomic electrons can absorb photons ONLY if the photon energy matches exactly an allowed transition between energy levels
  • Collision: a fast-moving electron from outside the atom (e.g. a beta particle) collides with an atomic electron, transferring some energy to it and exciting the atomic electron. The fast electron’s energy need not match exactly the atomic energy transition because the fast electron can recoil at a slower speed, retaining any surplus energy whereas a photon has to be absorbed entirely.

 

Higher (excited) energy states are unstable. An electron in an excited state will drop to a lower energy level provided a space is available (DE-EXCITATION.) Since the de-exciting electron is losing energy, it emits a photon whose energy exactly equals the energy lost by the electron. i.e. exactly equals the energy transition within the electron.

 

Line Spectra

 

Only photons with certain discrete energies can be absorbed or emitted.

 

The energy of a photon is linked to its frequency/wavelength: E = hf = hc/λ

 

Therefore only photons with certain wavelengths are emitted or absorbed by each different type of atom. This leads to discrete line spectra (c.f. continuous spectra from incandescent sources where photons are emitted across a continuous range of wavelengths.