Question

We often must make devices, tools, machines. Many times it is due to limited resources. The answer is based on CREATIVITY

Design a micro ruler or pattern that can be used for measuring and calibrating optical / electron microscopes. They exist. Research and make proposal or drawing. I.E What type and size of markings / shapes?

We have an air compressor. It is having problems overheating. How should we test what is going wrong with it.  What can we do to cool the tool if it is not repairable in a cost effective way?   You may use any needed tools and parts less than $100 each.

Answer 1

for an electron microscope
wavelength of electron can theoretically be infinitely smaller
but for the common microscopes
is about 2.5 pm for the microscope workng at about 200 keV

hence
for this wavelength, we can have a diffraction grating with n lines per m such that
and 1/m is of the order of the wavelength of electrons
hence
m = 4*10^11 lines per m

now from the periodic table
we can see that none of the elements have such small lattice constants

consider
Antimony

if antuimony crustal is used as diffraction grating for the electron microscope
then for maxima
d = 430 pm
thetam = arcsin(sin(thetai) - n*lambda/d)
for n = 1, thetai = 30 deg, and thetam = 29.616 deg

hence
an antimony diffraction grating which refelcts electrons frfom the microsope off itself ad trhen bounces off an electron counter screen ( 2 d sensor)

for the maxiomas obtained a valid value of lambda for electrons is obtained and then we can calibrate the electron microscope for the wavelngth of electrons for applied voltage