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Pickled_Gorilla
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Homework Statement
A collection of neutrons, nominally at rest, are confined in a region 1.0 nm wide on the x-axis at a height of 50 cm above a neutron detector. The neutrons are released and fall under the influence of gravity towards the detector which records the horizontal position of the hits. Estimate the width of the region of the detector that gets hit by neutrons.
Homework Equations
(1) E0 neutron = 939.57 MeV
(2) E = p2/2m
(3) p = h/λ
(4) a sin(θ) = mλ, a is slit width (1 nm)
(5) y= Dmλ/a, y is distance on detector, D is distance to detector from slit (50 cm), and a is slit width (1 nm)
The Attempt at a Solution
I treated this problem as a single slit diffraction problem.
Since the neutrons are initially at rest, their energy is E0.
Using (2) to find p, and then (3) to solve for λ gives 9.331 * 10-16m.
Setting sin(θ) = 1 to find the maximal minima, (4) becomes m = a/λ, and solving for m gives 1.07*106.
Plugging into (5) gives 0.5 meters, and since this is the distance in one half of the picture, the number is doubled for the total area. Thus the total area on the detector hit by neutrons is 1 meter.
Am I approaching this problem correctly?