# Electron Velocity Diffraction Grating Problem

## Homework Statement

Suppose that visible light incident on a diffraction grating with slit distance (space) of $0.01*10^{-3}$ has the first max at the angle of $3.6^{o}$ from the central peak. Suppose electrons can be diffracted with this same grating, which velocity of the electron would create the same diffraction pattern as this visible light?

## Homework Equations

d*sin(theta) = m(lamba)

## The Attempt at a Solution

I am thinking of using equations like $d\sin(\theta) = m\lambda$, but I am not sure where the angle comes into play here.

Obviously,

$(0.01 mm)(\sin(3.6)) = m\lambda$, but this doesn't help much?

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Suppose that visible light incident on a diffraction grating with slit distance (space) of $0.01*10^{-3}$ has the first max at the angle of $3.6^{o}$ from the central peak. Suppose electrons can be diffracted with this same grating, which velocity of the electron would create the same diffraction pattern as this visible light?

## Homework Equations

d*sin(theta) = m(lamba)

## The Attempt at a Solution

I am thinking of using equations like $d\sin(\theta) = m\lambda$, but I am not sure where the angle comes into play here.

Obviously,

$(0.01 mm)(\sin(3.6)) = m\lambda$, but this doesn't help much?
use the grating equation to find out the wavelength of the diffraction pattern -given out with light.
suppose you wish to have the same pattern with electron beam - then the wavelength associated with electron should be same.
can the the electron have wave property?
if it can then how wavelength depends on its velocity/energy/momentum?
the lambda should be related with velocity

jtbell
Mentor
equations like $d\sin(\theta) = m\lambda$,
A friendly tip: to show your equations inline with text, enclose your LaTeX equations in ##, not $. To show them as separate "paragraphs", use $$. Thanks. Okay:$$0.01\sin(3.6) = m\lambda$$so m=1, and thus$$\lambda = 6.279*10^{-7} m$$Then by De Broglie,$$\lambda = h/mv$$Thus,$$v = \frac{6.63*10^{-34}}{(9.1*10^{-31})(6.279*10^{-7})} = 1.16 m/s$\$

Is this right?

Thus,

v=6.63∗10−34(9.1∗10−31)(6.279∗10−7)=1.16m/s​
v = \frac{6.63*10^{-34}}{(9.1*10^{-31})(6.279*10^{-7})} = 1.16 m/s

Is this right?
i have not checked your numbers but theoretically the idea is same