Using Kaufmann and Bucherer's Data to Relate E, p & m

In 1901, W. Kaufmann did an experiment to investigate the relationship between velocity and mass for electrons in the 0.7MeV to 1.6 MeV energy range (W. Kaufmann, Gottingen Nach. 2, 143; 1901). Later, A. H. Bucherer did a similar experiment which included lower energy electrons (A. H. Bucherer, Ann. d. Phys. 28, 513; 1909).

In each case, deflection of electrons by a magnetic field yields momentum information while deflection by an electric field gives energy information. Thus, we can adapt the data of Kaufmann and Bucherer to show the relationship between E and p. We include simulated data for energies close to the electron rest energy to make your graph clearer.

To view and analyze the data, go to the data page.


  1. How can you use graphical analysis to discern a relationship between E and p using this data?
  2. What sort of function is a graph of E vs. p? of E2 vs. p2?
  3. What is E when p = 0? What does this indicate?
  4. What does the relationship between E and p look like when E is much greater than the rest energy?
  5. Can you infer a mathematical relationship between E, p, and m?