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
([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.