Energy Levels, Photon Emission and Wave Particle Duality

Energy Levels, Photon Emission and Wave Particle Duality

Emission spectra

Using diffraction grating and a spectrometer it is possible to look at the emission spectrum from a light source.

The emission spectrum looks like a continuous spectrum of colours if all possible wavelengths of light are present:

Hot gases, on the other hand, only emit specific, characteristic colours of light:

Within an emission spectrum, each line represents an electron moving from a higher energy level to a lower one. In order to achieve this, the electron emits a photon of light. The energy of this photon is equal to the difference in energy between the two energy levels involved:

hf = E1 – E2

In which:

  • h = the Plank constant (6.63 x 10-34Js)
  • f = the frequency of the photon in hertz (Hz)
  • hf = the energy of the photon in joules (J)
  • E1 = the energy of energy level 1 in joules (J)
  • E2 = the energy of energy level 2 in joules (J)

Absorption spectra

If white light is passed through a gas, specific wavelengths of light are absorbed by this gas. This effect can be seen from light emitted from the Sun: at first it appears to be a continuous spectrum. However, when you look more closely, it can be seen to consist of dark lines:

Wave-particle Duality

Light can act as both a wave and a particle:

  • diffraction can be explained when light is considered to be a wave
  • the photoelectric effect can be explained when light is considered to be a particle

Therefore, when considering light, you need to use the concept of wave-particle duality.


It is possible to calculate the momentum of a particle in kilogram metres per second (kg m s-1) with the following equation:

momentum = mv

In which:

  • m = mass in kilograms (kg)
  • v = velocity in metres per second (m s-1)

The De Broglie wavelength

De Broglie put forward the idea that all particles, not only light, exhibit wave-particle duality. It is, therefore possible to calculate the wavelength of all particles (the De Brogiel wavelength) with the following equation:

? = h / mv

In which:

  • ? = the De Broglie wavelength of the particle in metres (m)
  • h = the Plank constant (6.63 x 10-34Js)
  • m = the mass of the particle in kilograms (kg)
  • v = the velocity of the particle in metre per second (ms-1)