# 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.Questions:

- How can you use graphical analysis to discern a relationship between E and p using this data?

- What sort of function is a graph of E vs. p? of E
^{2}vs. p^{2}?

- What is E when p = 0? What does this indicate?

- What does the relationship between E and p look like when E is much greater than the rest energy?

- Can you infer a mathematical relationship between E, p, and m?