Finding mass of charged particle - magnetic field

[scholio]

Homework Statement

an isotope separator is used to separate charged particles having different masses. assume that two types of particles enter a region of constant magnetic field with the same kinetic energy, and assume that all particles have the same charge.

the radius of the circular path followed by the heavier particles is found to be 1.1 times that for the lighter particles. what is the ratio of their masses?

Homework Equations

kinetic energy U = 1/2(CV^2) = KE = 1/2(mv^2) where C is capacitance, V is electric potential, m is mass, v is velocity

radius r = mv/qB where q is charge, B is magnetic field

The Attempt at a Solution

i set up two relationships using both equations for each particle, the lighter and the heavier.

lighter particle:

r = mv/qB = ---> v = rqB/m ---> KE = 1/2(mv^2) = 1/2(m(rqB/m)^2) = (rqB)^2/2m

heavier particle:

i want to use the r = mv/qB but since both particles have same kinetic energy, the mass will be greater but the velocity will be lower than that of the lighter particle.

what would be the best way to determine the mass and velocity of the heavier particle? should i assume an arbitrary amount, say two times greater?

is my approach for the lighter particle along the right lines, or is there a better way?

 

[physixguru]

First answer me this:

An electron and a proton are injected into a uniform magnetic field at right angles to the direction of the field with the same Kinetic Energy. Then:
a)the electron trajectory will be less curved than the proton trajectory
b)the proton trajectory will be less curved than the electron trajectory
c)both the trajectories will be equally curved
d)both the trajectories will be straight.

Once you get this, go ahead.


The angular frequency of a charged particle in a uniform magnetic field is independent of its velocity or energy.This is also known as cyclotron theory.
Heavier the particle is , larger is its radius ; faster a particle is , larger is the radius.

Where does the confusion lie?

You are on the right track.Go ahead.

 

[rl.bhat]

Can you find the relation between momentum and kinetic energy?

 

[scholio]

physixguru:

"b)the proton trajectory will be less curved than the electron trajectory" - because proton has greater mass than electron thus less affected by magnetic field

a little confused about how the problem is stated, i can't really assume the two particles are either both electrons or both protons because one is heavier, yet they share the same charge.

rl.bhat:

momentum p = mv
kinetic energy KE = 1/2(mv^2)
so KE = 1/2(p^2) ??

 

[rl.bhat]

so KE = 1/2(p^2) ??
This is wrong.
KE = 1/2(p^2)/m or p = (2mE)^1/2...(1)
radius r = mv/qB where q is charge, B is magnetic field
This can be written as p = qBr...(2)
Compare eq. 1 and 2 and find the ratio of the masses. Note that the KE is same for both the masses.