Resolving proteins with UV microscope

[Les talons]

Homework Statement

Your molecular biology lab studies proteins, and you're frustrated because your microscopes can't quite resolve crystallized proteins. A sales rep touts the advantages of an expensive microscope using 200-nm ultraviolet light, saying you'll be able to resolve structures less than half the size that's resolvable with your optical microscopes.

Is the sales rep correct?
no
yes

Homework Equations

Rayleigh criterion
slit: Θ_min = λ/a
circular aperture: Θ_min = 1.22λ/D
X-ray diffraction: 2dsinΘ = mλ

The Attempt at a Solution

I looked up the wavelength ranges of visible light and found 390nm to 700nm. I also found the average size of a protein to be 531 angstroms or 5.31x10^-8 m. I also heard that you can resolve an object as small as one fourth of the wavelength from somewhere, is this true (can't find anything in the book or online anywhere on this point)? So I thought the answer is the sales rep is correct because the protein length is larger than the wavelengths of visible light. Is this correct thinking? There is not really enough given in the problem to use the equations, so I am led to believe there is some other information I missed somewhere. Thank you.

 

[haruspex]

A sales rep ... saying you'll be able to resolve structures less than half the size that's resolvable with your optical microscopes.

Is the sales rep correct?

The rep made a specific statement, and you are asked to comment on that. The statement says nothing about proteins.
I don't know whether this helps much, though. At least it avoids any question of what wavelengths the protein crystals absorb.

 

[Les talons]

For optical microscopes, the resolvable structures would all be in the visible spectrum of wavelengths. Comparing half of the minimum wavelength of the visible light is 390 nm /2 = 195 nm, to 200 nm of the UV light. Because 195 < 200, the sales rep. is right?

 

[haruspex]

390 nm /2 = 195 nm... Because 195 < 200, the sales rep. is right?

Based purely on that, the sales rep would be wrong, no? But most visible light has longer wavelengths, and I do not see universal agreement on the 390 figure. Remember that you need to be able to observe it somehow. For the UV, that will involve some UV detector, whereas for an optical microscope you'll be using the human eye. Not everyone has the same colour range.