# In which experiments the charge to mass ratio of proton was determined?

Are there experiments where the charge to mass ratio for protons have been determined in the same way as in Thompson’s experiments (where he determined the charge to mass ratio of electron) but with protons instead of electrons? Which experiments are performed to determine the charge to mass ratio of proton? Maybe somebody has pdfs of Thompson’s papers where he was reporting about the charge to mass ratio of proton and hydrogen ions.

## 1 Answer

I am not sure if Thompson ever determined the charge-to-mass ratio of a proton, but currently, the most precise measurements of the charge-to-mass ratio of a proton still use a magnetic field like Thompson, but rely on measuring (cyclotron) frequencies rather than deflection. As frequencies are the quantities that can be determined most accurate (see the Nobel lecture of Hänsch: “Never measure anything but frequency!” ), the result is much more precise.

The charge-to-mass ratio ($q/m$) is obtained from the cyclotron frequency of a proton in an magnetic field $B$. The cyclotron frequency is associated with the motion of a charged particle in the plane perpendicular to the magnetic-field direction and is given by

$\nu_c=\frac{qB}{2\pi m}$.

See for instance Phys. Rev. Lett. 74, 3544 (1995).

• Thanks! I cannot find confirmation that Thompson had measured the charge-to-mass ratio of a proton. In many sources it is claimed that the charge-to-mass ratio of a proton was determined by W. Wein. But, there is also publication that actually W. Wein determined the charge-to-mass ratio for a mixture of nitrogen and oxygen, as residual gases (rsc.org/education/eic/issues/2010May/…). In paper from 1913 Thompson simply used most deflected line, assuming that is hydrogen ion, for calculation of masses for others ions. – VYT Nov 25 '15 at 17:51