Some students visualise an electron as a smeared cloud of charge

Quantum and Nuclear


In studies, this has presented itself in the following ways:

  • Students saw the probability as a subjective lack of knowledge (e.g. Bethge 1988) and therefore thought of smeared orbits along the maxima of the wave function.
  • Uncertainty is a consequence of the fact the electron is 'smeared out', not because of the non-vanishing commutator of certain pairs of variables.

Resources to Address This

  • This teaching guidance resource introduces the idea of wavelike behaviour being associated with electrons and the Complementary principle.

    It can be used to start a discussion about whether there are separate particle or waves or whether behaviour is more complex than this.

    View Resource
  • This lesson-based activity introduces the idea that electrons can be represented as standing waves. It stars with a refresher about Melde’s experiment, setting up a standing wave in a string under tension and then applies this idea to electrons using a wire loop. The resource also provides a set of calculations based on the information, linking to the de Broglie equation. 

    This material should be linked with concepts from the photoelectric effect to show the complementary behaviour of electrons.

    View Resource
  • This lesson outline introduces the student to the photoelectric effect, from the basic phenomenon to an explanation of the effect including the concept of work function and the photoelectric equation. A range of worksheets and questions are provided.

    Use these ideas to discuss whether the electron and photon are behaving in a wavelike or particle like way.

    View Resource


  • Petri, J. & Niedderer, H., () A learning pathway in high‐school level quantum atomic physics, International Journal of Science Education, 20 (9) 1075-1088,

    DOI: 10.1080/0950069980200905.

  • Müller, R. and Wiesner, H., () Teaching quantum mechanics on an introductory level, American Journal of Physics, 70 (3) 200-209,

    DOI: 10.1119/1.1435346

  • Greca, I. M. and Freire Jr., O., () Does an Emphasis on the Concept of Quantum States Enhance Students' Understanding of Quantum Mechanics? Science & Education, 12, 541-557,

    DOI: 10.1023/A:1025385609694

  • Bethge, T., () Aspects of students' matrix of understanding of basic concepts in atomic physics, Doctoral dissertation, University of Bremen.

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