# DeBroglie matter waves and double-slit

## Homework Statement

A beam of electrons with a kinetic energy 1.00 MeV strikes normally at an array of atoms separated by 0.25 nm. in what direction can we expect the electrons in the fifth order?

Ek= hf - W
p=h/λ
dsinθ=nλ

## The Attempt at a Solution

i tried my hardest, but i didnt know where to start

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Your last equation is for working out the angular position, θ, of the interference maxima when you have waves that are normally incident on a diffraction grating. I think the idea here is that the spaces between the atoms work like gaps in a diffraction grating so it's not quite a double slit set up like you described in the title - but no matter, just use that last equation to find the angle when n = 5.

Your problem is that you don't know the wavelength of the electrons. I suspect that things get a bit more complicated because at 1 MeV the electrons are going to be moving fast enough that you're going to have to take special relativity into consideration when finding the momentum. You need the momentum to get the wavelength with your second equation. I'm not sure what to do with your first equation - it looks like the the equation that describes the photoelectric effect and I'm not sure that it fits in anywhere.

Anyway, do you have any special relativity type equations are to do with the energy of a particle?

PS

When I work though this I get a really neat answer - I think you just have to work through some large and messy numbers to get there!

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