Electron Scattering

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Homework Statement


Assuming that in electron scattering off a target proton you need to resolve a distance
scale below R = 10^-15 m (that is, the uncertainty in the proton’s position is no larger than
about 10^-15 m), determine a condition on the electron momentum, and justify it in one or
two sentences. Decide if this corresponds to a relativistic or a non-relativistic situation

Homework Equations


([tex]\Delta[/tex]p)([tex]\Delta[/tex]x) [tex]\geq[/tex] hbar/2


The Attempt at a Solution


[tex]\Delta[/tex]x = 10^-15
[tex]\Delta[/tex]p [tex]\geq[/tex] hbar/(2*[tex]\Delta[/tex]x) = 5.273*10^-20


I'm not sure I completely understand the question. If I got this right, it's because I saw what my book did and took a guess; I'd rather understand what's going on.

I understand the uncertainty principle for the target proton, but I don't understand how those uncertainties translate to the uncertainty of the electron.
Also, a simple point of confusion related to the topic: when is [tex]\Delta[/tex]p = p or [tex]\Delta[/tex]x = x? I've seen these down in solutions in what appears to be a haphazard fashion. I'd be very gracious for any insight into that.

Thank you for any help.
 
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Answers and Replies

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I understand the uncertainty principle for the target proton, but I don't understand how those uncertainties translate to the uncertainty of the electron.
Good question. This is actually a little weird: the [tex]\Delta x[/tex] isn't really referring to the proton (per se) at all. Think about it more like: 'in general, to resolve anything with [tex]\Delta x[/tex] positional accuracy....'
You're using the electron itself as a measurement tool.
This certainly isn't an obvious answer, and the details get even uglier: e.g. what the given accuracy can actually tell you about the proton.... etc.

Also, a simple point of confusion related to the topic: when is [tex]\Delta[/tex]p = p or [tex]\Delta[/tex]x = x? I've seen these down in solutions in what appears to be a haphazard fashion.
In the context of the uncertainty principle, they should always be deltas (i.e. [tex]\Delta x[/tex]). Often, however, with something like momentum people often assume that the uncertainty is comparable to the value, i.e. [tex]\Delta p \approx p[/tex], but this is an approximation and a generalization.
The other explanation is people just being lazy---and this happens to.
 

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