The neutron interference pattern of figure p39.45 was made by shooting neutrons

Question

The neutron interference pattern of figure p39.45 was made by shooting neutrons with a speed of 200 m/s through two slits spaced .10mm apart.
a. what was the energy, in eV, of the neutrons?
b. what was the de broglie wavelength of the neutrons?
c. The pattern was recorded by using a neutron detector to measure the neutron intensity at different positions. Notice the 100 micrometer scale on the figure. By making appropriate measurements directly on the figure, determine how far the detector was behind the slits.The neutron interference pattern of figure p39.45 was made by shooting neutrons with a speed of 200 m/s through two slits spaced .10mm apart.
a. what was the energy, in eV, of the neutrons?
b. what was the de broglie wavelength of the neutrons?
c. The pattern was recorded by using a neutron detector to measure the neutron intensity at different positions. Notice the 100 micrometer scale on the figure. By making appropriate measurements directly on the figure, determine how far the detector was behind the slits.

Explanation / Answer

Given speed of neutrons v = 200 m/s distance between two slits d = 0.10 mm = 0.1*10^ -3 m a) energy of neutrons is              E = ( 1 /2) m v 2                 = 0.5(1.6*10^ -27 kg )( 200 ) 2                   =3.2*10-23 J                 = 2*10^-4 eV   b)    momentum of neutroni s                P = 2 m E                     = 2( 1.6*10 ^ - 27 kg) ( 3.2*10 ^ -23 J )                      = 10.24*10^ -25 kg m/s       de-broglie wavelength               = h / P                   = ( 6.635*10-34 J s ) / ( 10.24*10^ -25 kg m/s )                   = 0.65 nm

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