# Distance between Isotopes in a mass spec

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1. Mar 11, 2016

### Elvis 123456789

1. The problem statement, all variables and given/known data
Suppose the electric field between the plates P and P' in the mass spectrometer in following figure is 1.89×104V/m and the magnetic field in both regions is 0.668 T.

If the source contains the three isotopes of krypton, 82Kr,84Kr, and 86Kr, and the ions are singly charged, find the distance between the two adjaicent lines formed by the three isotopes on the photographic plate. Assume the atomic masses of the isotopes (in atomic mass units) are equal to their mass numbers, 82, 84, and 86. (One atomic mass unit = 1u = 1.66×10−27kg.)

2. Relevant equations
v = E/B

R = mv/qB

3. The attempt at a solution

I found that the selected speed (v) is 2.83 * 10^4 m/s

I got 0.0360 m for the radius of 82Kr

0.0369 m for 84Kr

and 0.0378 m for 86Kr.

My problem is that I don't even understand what it is that they are asking for. What are these adjacent lines that they are talking about? and if theres three isotopes, shouldn't there be three lines?

2. Mar 11, 2016

### Staff: Mentor

You haven't included the image so I can't be certain, but usually the ions that are selected will follow circular arcs of radii that depend upon their mass before they impact on a target. Where they impact they produce an image, either a spot or line depending upon details of the equipment. Presumably they are looking for the distance separating such individual lines. If it turns out that the spacing is even, then any two adjacent lines will do. Perhaps the problem text should have read, "...find the distance between the two adjacent lines formed by the three isotopes..."

3. Mar 11, 2016

### Elvis 123456789

sorry I forgot about the image.

https://session.masteringphysics.com/problemAsset/1266175/5/22.jpg
Sorry I forgot about the picture.

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4. Mar 11, 2016

### Staff: Mentor

Okay, it looks like I was correct; You want to find the distance between adjacent impact locations on the particle detector target.

5. Mar 11, 2016

### Elvis 123456789

Wouldn't that be the difference in radii between two adjacent isotopes? For instance, (Radius for 84Kr) - (Radius for 82Kr) = 0.9 mm?

6. Mar 11, 2016

### Staff: Mentor

Examine the diagram carefully. How far from the selector exit port do the ions land? Is it one radius away?

7. Mar 11, 2016

### Elvis 123456789

ah I see, they all land one diameter away. so 2*[(Radius of 84Kr) - (Radius of 82Kr)]?

8. Mar 11, 2016

### Staff: Mentor

Sure.

9. Mar 11, 2016

### Elvis 123456789

Ok awesome, thank you kind sir.