What is the ratio of radii for the two species X+ and X2+?

[KatieD]

Homework Statement

The ion source is a spectrometer produces both singly and doubly ionized species, X+ and X2+. The difference in mass between these species is too small to be detected. Both species are accelerated through the same electric potential difference, and both experience the same magnetic field, which causes them to move on circular paths. The radius of the path for the species X+ is r1 while the radius for species X2+ is r2. Find the ratio r1/r2 of the radii.

So this means:
m1=m2
V1=V2
B1=B2

Homework Equations

r=mv/qV

The Attempt at a Solution

We know that the charge of the X2+ is twice the X. I am just so confused about where to go from here. My teacher has written out the solution but it still makes no sense.

Please help :(

Katie

 

[LowlyPion]

You just about have it with your equation don't you?

Consider the equation for each particle.

Now take the ratio of the equations.

If the masses are virtually identical, the acceleration through the electrical potential and hence the velocities are also the same then aren't they?

By the time you get through canceling things out it looks to me like you can determine r1/r2 by inspection.

 

[KatieD]

so here's where i am at:

r1=mv/qB
r2=mv/2qB

I then divide r1 and r2 getting
((m1v1)/(qB))/((m2v2)/(2qB))

then with canceling out I get r1/r2=2

I am confused, the teachers notes say its the square root of 2, I am not sure where this comes in

 

[LowlyPion]

so here's where i am at:

r1=mv/qB
r2=mv/2qB

I then divide r1 and r2 getting
((m1v1)/(qB))/((m2v2)/(2qB))

then with canceling out I get r1/r2=2

I am confused, the teachers notes say its the square root of 2, I am not sure where this comes in

Oops. Sorry. The acceleration through the electrical potential will result in a velocity that is not identical. It will be different how?

 

[KatieD]

EPE= Vq
so if the force goes up... and the mass is the same the acceleration will have to go up with the second one by 2 right?

 

[LowlyPion]

EPE= Vq
so if the force goes up... and the mass is the same the acceleration will have to go up with the second one by 2 right?

I think they want you to accelerate that from rest. So ...

W = q*ΔV = 1/2*m*v²

Which means that the ratio of v² = 2:1, since v² is proportional to the charge.