# Carbon ions in Tandem Accelerator

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1. Aug 26, 2014

### Dreggovich

Hi all I'm new to this forum, there seem to be quite some knowledge here. I hope someone can help shed some light on this. I took this exam about a week ago and I had no idea on how to solve this question, and I haven't been able to figure this one out since.

1. The problem statement, all variables and given/known data
In a tandem accelerator a negatively charged carbon ion is accelerated towards the positive potential (+3MV). In the middle of the accelerator there is a volume with Argon gas in which the carbon ion looses electrons and leaves with +3 charge. A similar potential difference on the other side of the argon chamber with the positive plate closest to the chamber on both sides. (I hope this is understandable).

a) Calculate the velocity of the negative ion when it reaches the argon chamber, also calculate the speed at which it leaves it leaves the accelerator (passing both acceleration zones). Do this calculation for both carbon 12 and 14.

b) The accelerator is followed by a magnet to separate the different carbon isotopes. The magnet is a dipole-magnet with the field strength of 1 Tesla orthogonal to the carbon ions path. What is the path radius for the two isotopes?

c) The mass spectrometer uses the different masses of the isotopes, why do the isotopes have different mass?

2. Relevant equations
I am at a loss here I'm sure I need to use the rest mass from the tables and I would be surprised if I'm not meant to use p=\gamma m_0 v and E_{tot}^2=(pc^2)+(mc^2)^2 for question a.
I'm obviously missing something.

For the second question I'm haven't gotten anywhere. I can't find anything remotely similar in the lecture notes. And the third one must be as simple as the extra neutrons in carbon 14.

3. The attempt at a solution

Im sorry I haven't gotten anywhere with this even though I've been trying for almost a week and I have never felt this dumb I was supposed to do this and 5 other questions of the same caliber in 5 hours and I have not been able to figure this one out in maybe 13 hours of trying with lecture notes and the internet at my disposal.

2. Aug 26, 2014

### BvU

Why don't you try a non-relativistic approach first, then check if the velocity is small enough compared to c ?

Working in MeV is quite comfortable in this case: a charge of one e accelerated over 3 MV picks up 3 MeV of kinetic energy etc etc.

Last edited: Aug 26, 2014