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erok81
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Homework Statement
In a double slit experiment, a beam of neutrons with speed 0.6m/s is diffracted by two apertures which are 0.05μm apart.
a. What is the neutron wavelength?
b. Where does the first minimum appear?
Homework Equations
[tex]\lambda = \frac{h}{p}[/tex]
[tex]dsin\theta =(m+\frac{1}{2})\lambda[/tex]
The Attempt at a Solution
First off for the wavelength.
[tex]\lambda = \frac{h}{p}[/tex]
I had to calculate p first. Which is just mv -> (1.657x10-27)(0.6) = 9.942x-28
Plugging that into the de Broglie wavelength forumla...
[tex]\lambda = \frac{h}{p} = \frac{6.63\times10^{-34}}{1.005\times10^{-27}} = 6.6\times10^{-7} [/tex]
That answers part a.
Now part b I am stuck on. First I don't know how far away the detector is, so I can't really give a definite location. So I was just going to go with the angle.
Using [tex]dsin\theta =(m+\frac{1}{2})\lambda[/tex] with m= 0
I get...
[tex]sin^{-1}\left[\frac{1}{2}\times\frac{6.6\times10^{-7}}{0.05\times10^{-6}}\right] = sin^{-1}(sin{\theta})[/tex]
Before taking the arcsin I have a value of 6.597. Which obvisouly gives me a weird answer for theta. Weird answer being 1.571° and -2.574°.
Any ideas where I am going wrong?
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