00:01
All right, so we have a singly charged ion with a mass m, and let's say it has a charge q, which is really like the electron mass.
00:11
And it is accelerated from rest through a potential difference of delta v, and then deflected by a uniform magnetic field into a semicircle that has a radius of r.
00:24
And so now we're, have the same scenario, same potential difference, same magnetic field.
00:31
But we have a triply charged ion.
00:34
So the charge of the new particle, it's called us q prime, is equal to 3 times e.
00:41
And it goes into a radius, we'll call this r prime, of 5r.
00:46
And so we want to know what's the ratio of the masses of the two ions.
00:50
So let's see this has a mass of m prime.
00:52
Well, the radius of the orbit that it goes into, so the particle, when it enters into the magnetic field, experiences a centripetal force of m v squared over r and this is equal to the charge on the particle times the velocity it's moving at times the magnetic field strength so if we solve this for the radius which is really kind of the relevant variable we want it's going to be mv over qb okay so for either particle it's going to be this now we know the velocity of the the particle v is like the the kinetic energy the particle gains, let's put it this way, is one -half mv squared.
01:33
This is equal to the charge of the particle times the accelerating potential.
01:37
So you can see the velocity is like the square root of 2q delta v over m...