Physics/De broglie wavelength
Neutrons traveling at 0.400 m/s are directed through a pair of slits separated by 1.00 mm. An array of detectors is placed 10.0 m from the slits.
a) What is the de Broglie wavelength of the neutrons?
b) How far from the axis is the first zero-intensity point on the detector array?
c) When the neutron reaches a detector, can we say which slit the neutron passed through?
The deBroglie wavelength of a neutron is given by:
The angle at which the first minimum occurs will be given by:
n*lamba=d*sin(theta) where n=1/2
Therefore, the angle at which the first minimum occurs will be:
Since this angle clearly falls within the small angle approximation sin(theta) can be replaced by theta which can in turn be replaced by x/L where L is the distance to the screen and x is the distance from the central antinode and the first minimum.
Solving for x:
c) This cannot be determined since the neutron wave did not go through either slit! As a wave it went through both slits. I you position a detector in an attempt to determine whether or not the neutron went through a particular slit the interference patter goes away!