Discovery of the Anti-Electron - Question

Question

I have a general question concerning the description of a Figure, taken from Griffiths' Introduction to Elementary Particles, page 20:

I'm afraid I do not really understand the last part: How is it possible to determine the mass of the particle by looking at the curvature of the track? I mean, the only question that I know is $$\left| \mathbf{p}\right| \approx 0.3 \cdot B\cdot R,$$ relating the three-momentum of a particle in a magnetic field $B$ and the strength of the curvature $R$ to each other. Where does the mass enter, is it by saying that $$\left| \mathbf{p}\right| = m\cdot v \qquad (\star)$$

But then, why am I allowed to use $(\star)$, don't we have to be relativistic? And even if we were allowed to use $(\star)$, how would we determine the velocity $v$?

Answer 1

Equating the force on a charged particle with the centrifugal force in the circle in a magnetic field, gives

$Bqv=mv^2/R$

one has the momentum.

The "texture" in the text you provide, is the ionisation of the medium through which the track passes, which is different for different masses, and can be used in determining the order of magnitude of the mass in the simple experiment you quote.

Here is a book reference:

The ionization loss dE/dx is a function only of the velocity v of the particle (for a given charge), so that a simultaneous measurement of dE/dx and of the momentum p enables determining the mass m of the particle.