Magnetic Forces and Magnetic Fields (mass spectrometer)

In summary, the problem involves two isotopes of carbon, carbon-12 and carbon-13, that are singly ionized and given a speed of 6.667x10^5 m/s. They enter the bending region of a mass spectrometer with a magnetic field of 0.8500T and the goal is to determine the spatial separation between the two isotopes after they have traveled through a half circle. The correct approach is to draw a diagram of the spectrometer and calculate the difference between the diameters of the two circular paths of the ions, which will give the spatial separation. The separation is not given by the difference between the radii of the circles, as they do not have the same center.
  • #1
CaffeineNut
5
0

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!
 
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  • #2
Anyone? =/
 
  • #3
Draw a picture. Is it r1-r2 or d1-d2?
 
  • #4
There is no picture associated with this problem.
 
  • #5
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?
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
CaffeineNut said:
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.
 

1. What is a mass spectrometer?

A mass spectrometer is a scientific instrument used to measure the mass-to-charge ratio of ions. It works by ionizing a sample and then separating the ions through an electric and magnetic field, allowing for the identification and quantification of different substances within the sample.

2. How do magnetic forces play a role in a mass spectrometer?

Magnetic forces are crucial in a mass spectrometer because they are responsible for separating the ions based on their mass-to-charge ratio. The ions are deflected by a magnetic field, with heavier ions being deflected less than lighter ions. This allows for the identification of different substances within a sample.

3. What is the difference between a magnetic force and a magnetic field?

A magnetic force is the force exerted on a charged particle by a magnetic field. A magnetic field, on the other hand, is a region of space where a magnetic force can be observed. It is created by moving electric charges and can be visualized as lines of force that point from the north to the south pole of a magnet.

4. How is a mass spectrometer used in scientific research?

Mass spectrometers are used in a wide range of scientific research, including chemistry, physics, biochemistry, and environmental science. They can be used to identify unknown substances, measure the isotopic composition of elements, and analyze complex mixtures of substances. They are also used in the analysis of biological molecules, such as proteins and DNA.

5. Can a mass spectrometer be used for medical purposes?

Yes, mass spectrometers are commonly used in medical research and diagnostics. They can be used to analyze blood and tissue samples for the presence of specific substances, such as drugs or disease markers. They are also used in the development and testing of new drugs and treatments.

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