How Do Electron Wavelengths Influence Diffraction Patterns?

[hmsmatthew]

Homework Statement

An electron is traveling at the "non-relativistic" velocity of 0.05 times the speed of light. Find its de Broglie wavelength. Explain what size an object needs to be in order to cause a stream of such electrons to form a significant diffraction pattern.

Homework Equations

Wavlength = h/mc

The Attempt at a Solution

The answer to the first part is easy, straight substitute and solve. However I cannot seem to find any answer on the second. My own take on this is that the object must be somewhere around the magnitude of the wavelength of the electron (like diffracting through a slit) and must be not be so thick as to completely deplete the electrons of their Kinetic Energy.

Any help would be greatly appreciated !

Matt

 

[Mindscrape]

Yes, I'm sure the question must be alluding to either a single slit diffraction pattern or a double slit (or your choice). Basically, either way you will have

$$dsin\theta=m\lambda$$

where you would want to use small angle approximation to get

$$d\theta=d\frac{y}{L}=m\lambda$$

You would just want a wavelength that will give a reasonable separation separation distance, and yes, I'd imagine it's within a few orders of magnitude of the electron mass.