Magnetic Forces and Magnetic Fields (mass spectrometer)

[CaffeineNut]

Homework Statement

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93x10^-27 kg and 21.59x10^-27 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 6.667x10^5 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.8500T. Determine the spatial separation between the two isotopes after they have traveled through a half circle.

Homework Equations

r = mv / (eB)

m = (er^2/2V)*B^2

The Attempt at a Solution

In this problem, I attempted to plug in the values I knew (B, e, v and m) in order to find the radius of each individual isotope. Then i attempted to obtain the difference in radius to obtain the spatial separation between the two isotopes, however I can't seem to obtain the right answer. I'm not really sure how else to approach this problem. Perhaps I am having trouble understanding what exactly they mean by "spatial separation." I was hoping someone could clarify what I'm doing wrong and how I should be approaching this problem differently. Below are my calculations:

r1 = (19.93x10^-27) * (6.667*10^5) / (1.6x10^-19 * 0.85)
r2 = (21.59*10^-27) * (6.667*10^5) / (1.6x10^-19 * 0.85)

r2 - r1 = spatial separation (?)
Correct answer for this problem: 1.6x10^-2 m.


Someone please shed some light on this problem. Thank you!

 

[CaffeineNut]

Anyone? =/

 

[Gokul43201]

Draw a picture. Is it r1-r2 or d1-d2?

 

[CaffeineNut]

There is no picture associated with this problem.

 

[Gokul43201]

I was saying that you need to draw a diagram of what is happening in the spectrometer for you to understand what exactly the separation is.

What happens to the ions after they enter the region of the B-field?

 

[CaffeineNut]

I understand that they travel half a circle, where some of the ions pass into a detector while other ions may travel an outer path and miss the detector.

Instead, could you perhaps shed some light on what exactly I'm doing wrong mathematically?

I assumed that if you subract that radius that each of the ions travel from one another then you should have found the distance between the ions themselves.

 

[Gokul43201]

Why the difference between the radii? They do not travel in concentric circles. If you draw the picture, you'll see that the separation is given by the difference between the diameters.

 

[CaffeineNut]

Oh, I was not aware that they don't start at the same center. This is rather unusual though given the picture outlined in Cutnell's physics book of a mass spectrometer. When the ions enter the B-field they enter from the same spot and thus appear as though they are initiating travel from the same point.

Thank you for this information. I believe now I can solve the problem.

 

[Gokul43201]

Oh, I was not aware that they don't start at the same center. This is rather unusual though given the picture outlined in Cutnell's physics book of a mass spectrometer. When the ions enter the B-field they enter from the same spot and thus appear as though they are initiating travel from the same point.

This is actually correct. They DO enter from the same point. But this is exactly the reason that their two circular paths do not have the same center.

Please draw a picture and label the start points, the centers of the two circles and the end points, and you'll see what I mean.