Estimating the energy of an alpha particle using Bethe's formula

PandaKitten
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Homework Statement
Full question is below
Relevant Equations
Bethe's formula
The question is below. I tried reasoning that because x is constant, E is also constant however that gives me values in the range of 10^51. Then I tried to use numpy's ivp_solve function to solve the differential equation however I wasn't able to get that working either. Apparently I'm meant to use Taylor's expansion to estimate E however I'm not sure how I would do that.
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PandaKitten said:
This is a simplified version which we were given because the alpha particle is non relativistic so beta << 1 and it also uses reduced mass mu and also E = 1/2 m_e/m_He.
This last statement is unclear. Please show what ## \mu ## is algebraically. Supposedly ## E ## is the energy of the alpha particle. This looks like a case where your notes that you might have taken in lecture contain errors.
 
This is what the question states
daww.png
 
I have to admit, I can't make sense out of their asking for a graph of ## -\frac{dE}{dP} ## vs. ## E ##. Perhaps someone else can see what they are asking for here.
 
PandaKitten said:
Homework Statement:: Full question is below
Relevant Equations:: Bethe's formula

The question is below. I tried reasoning that because x is constant, E is also constant however that gives me values in the range of 10^51. Then I tried to use numpy's ivp_solve function to solve the differential equation however I wasn't able to get that working either. Apparently I'm meant to use Taylor's expansion to estimate E however I'm not sure how I would do that.
View attachment 282789
Are you 100% sure they are asking a graph of -dE/dP vs E?? I would be willing to bet that this is a typo and they really are just asking a plot of -dE/dx vs E, which is then simple, they just want the graph of the expression they provided. (By the way, their definition of reduced mass is very unorthodox!)
 
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Charles Link said:
I have to admit, I can't make sense out of their asking for a graph of −dEdP vs. E. Perhaps someone else can see what they are asking for he
For instance, one might wish to choose a pressure where the response of the detector has particular characteristics for a certain energy alpha particle. Maybe there is a nice flat spot or an edge.
 
dE/dP makes no sense on its own. d2E/dPdx means something.
 
  • #10
They were asking in the context of a 10cm path length so I assume that is the detector path length and an average energy if I recall
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