In a Davisson-Germer experiment, a beam of neutrons (mass 
), each with kinetic energy 
,
travels toward a crystal of spacing d=3Å between atoms along its
surface. A detector of width 
counts the rate of the
total number of neutrons which enter it. The detector sits at a
distance of 
from the target crystal and detects neutrons
scattered at angles near 
from the surface. (See
Figure
2.)
Compute the spacing 
between the expected
interference maxima in terms of m, d, E, 
and h. By
observing the changes in the rate of the arrival of neutrons as the
position of the detector is varied, will the experimentalist be able
to detect the interference pattern of the scattered neutrons?
Hint: If you have an expression of the form 
,
differentiating both sides of the expression will allow you to
determine 
.
Figure 2: Davisson-Germer Apparatus