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Python and Rutherford Scattering 
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#1
Dec1012, 04:40 AM

P: 29

Hello everyone
I have been supplied with this eqn [tex]n=\frac{Nat}{16r^2}(\frac{2Ze^2}{4\pi\epsilon_0E_K})^2cosec^4(\frac{\ph i}{2})[/tex] for Rutherford scattering. [tex]N[/tex] is the number of alpha particles incident on a unit area of foil [tex]t[/tex] is the thickness of the foil [tex]a[/tex] is the number of atoms per unit volume within the foil [tex]r[/tex] is the distance of the detector away from the collision [tex]Z[/tex] is obviously the atomic number of the foil's material and [tex]E_k[/tex] is the kinetic energy of the incident alpha particles I need to use python to plot a graph of number of counts 'n' versus the scattering angle phi. To do this I need to create a GUI with entry fields for some of the above variables. This bit is not the problem. The problem is so far I cannot get the eqn to give a useful plot.These figures are not based on an actual experiment which I have had to carry out. These are all theoretical values for the purpose of the computer program. Could anyone suggest reasonable values for the above variables. Z is not necessary as I'm using 79 (gold). For example I've no idea how many atoms per unit volume there would be in a sheet of foil prepared for one of these experiments. Then if these reasonable values don't plot well either I will know that it is my code that needs looking at (which I'm sure is fine at the mo). Any help would be greatly...greatly appreciated. 


#2
Dec1012, 06:43 AM

Sci Advisor
P: 2,751

So there are 6.02E23/197 atoms per gram, and therefore 6.02E23/197*19.3 atoms per cm^3. This comes to about 5.9E22 by my quick calculation. 


#3
Dec1012, 06:57 AM

Sci Advisor
P: 2,751

My problem with that equation is that the density of strikes goes to infinity as theta goes to zero, which doesn't seem right. Unless it is an approximation that is only valid over a limited range of theta perhaps. Do you have any more information on the origins of that formula? 


#4
Dec1012, 09:50 PM

P: 891

Python and Rutherford Scattering
like uart said, the basic shape of the plot is not going to change if all you are doing is plotting phi vs n.
here is what it looks like using Wolfram. 


#5
Dec1212, 08:14 AM

P: 29

Thanks a lot uart. Not sure how my department has come up with the equation, tis probably some approximation for the purposes of the python exercise we have to do. You're right about the division by zero, I've had to make sure my range of angles does not include zero (which is stupid because most angles in this experiment would be zero)
Any way I achieved my plot, an exponentially decaying curve. Thanks again. 


#6
Dec1212, 08:24 AM

Mentor
P: 11,787




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