Quantum Physics: Electron Microscope

[10104863]

Quantum Physics: Electron Microscope

Homework Statement

Consider electrons in the accelerating voltage of 15 kV used in an electron microscope with a 'lens' diameter D = 0.5 cm and focal length f= 50 cm.
a) We require that the resolution is a tenth of the size of the object we want to study. What is the size of the smallest object that we can study with this electron microscope ?

b) Electrons in this microscope have wavelength λ_e. If we had photons with the same wavelength, λ_γ = λ_e, how would their energy compare to the energy of the electrons in the microscope ?

c) What is the momentum of photons with λ_γ = λ_e ?

Homework Equations

E = hc/λ
p = h/λ
There are definitely others that are needed but I don't know which ones.

3. Attempt
I don't even know how to begin with part a, so if anyone can give me some advice that would be great. You don't have to do the work for me, just tell me what to do and why.
For part b, I think the energy of the photon is hc/λ_γ, while the energy of the electron can be found through the equation E = h²/(2mλ_e²) so the result will depend on the wavelength, which I don't know.
Finally, for part c, I know that the momentum is p = h/λ_γ.

 

[sgd37]

The smallest object you can study focal distance away is given by $$1.22 \frac{f \lambda}{D}$$ where D is the diameter of the lens

the energy of the electron is given by $$qV$$ and you should be able to work out the wavelength from that and consequently the rest of the question