Traditionally, the way that physicists have discovered new sub-atomic particles

Question

Traditionally, the way that physicists have discovered new sub-atomic particles is by colliding two known massive particles in the presence of a magnetic field. If the two particles have sufficiently high kinetic energy, the result of the collision is that they break apart into many smaller particles which are sent flying outward from the collision. However, since there is a magnetic field perpendicular to the direction of the charges' velocity, the charges will simply travel in a circle under the magnetic force. (In reality, they spiral inwards because they dissipate energy as they travel through the detection chamber in the form of Cerenkov Radiation'. See diagram below-it is not abstract art but an actual collision event). Imagine that you discover a new particle which you assume to have a charge of +e (it is possible that its charge is actually has an integer multiple of e, but you can do other experiments to determine this). You see that in the presence of a uniform magnetic field B vector = 1.0 Tk cap, it circles around with a radius of 1.57 cm in the x-y plane. During the 1.0 ns camera exposure time, you estimate that the particle has traveled a total distance of 3.0 times 10^-5 m. Determine the mass of the particle that you have just discovered. Relate this to the mass of a proton: how many times greater or smaller is this particle's mass?

Explanation / Answer

Radius of circle of charged particle, moving in normal magnetic field
r = mv / qB
m is mass of particle, V is speed, q is charge of particle and B is magnetic field.
v = distance travelled / time = l/t
r = ml/qBt
m = q B r t / l
   = 1.6x10-19 * 1 * 1.57x10-2 * 10-9 / 3x10-5
   = 8.37 x 10-26 kg

Mass of proton = 1.67x10-27 kg
m/ mass of proton = 50.12
hence particle is 50 times heavier than proton

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