Electron Scattering: Resolve Distance Scale Below 10^-15 m

[UnIssued]

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

(\Deltap)(\Deltax) \geq hbar/2

The Attempt at a Solution

\Deltax = 10^-15
\Deltap \geq hbar/(2*\Deltax) = 5.273*10^-20I'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 \Deltap = p or \Deltax = 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.

 

[zhermes]

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 \Delta x isn't really referring to the proton (per se) at all. Think about it more like: 'in general, to resolve anything with \Delta x 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 \Deltap = p or \Deltax = 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. \Delta x). Often, however, with something like momentum people often assume that the uncertainty is comparable to the value, i.e. \Delta p \approx p, but this is an approximation and a generalization.
The other explanation is people just being lazy---and this happens to.