# Finding diffraction-limited spatial resolution

1. Oct 6, 2013

### leroyjenkens

1. The problem statement, all variables and given/known data

A scanning electron microscope (SEM) images samples using a beam of electrons. If
the electrons are accelerated across a potential difference of 5.00 kV, what is the
diffraction-limited spatial resolution of the SEM? Work this problem both relativistically and nonrelativistically.

2. Relevant equations
This is what I used, but I'm not sure what exactly to use.
$$E=eV$$
$$E=\frac{hc}{λ}$$
$$E=\frac{mv^{2}}{2}$$

3. The attempt at a solution
I first solved for E using E=eV, because I have both e and V, then I plugged that into the second equation to solve for wavelength (don't know why, I just wasn't sure what I'm supposed to be solving for. I understand what the question wants from me).

Then I set $eV=\frac{mv^{2}}{2}$, solving for velocity and found it to be 4.19x107.

Then I solved for E using $E=γmc^{2}$

But I'm not sure what the question wants me to find. What is diffraction-limited spatial resolution?

Thanks