Question

49. 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 off
axis is the first zero-intensity point on the detector array?
(c) When a neutron reaches a detector, can we say which
slit the neutron passed through? Explain.

Answer 1

@LastDayWork
I need help (for the moment) with part b.
Figured out part a, need to think about c.
\[\lambda = {h\over p}\]
lambda is the wavelength
h is lanck's constant
p is the momentum
This is wave-particle duality.

Answer 2

I THINK that is the idea....

Answer 3

This is the general diagram.
We are given that (SI Units)
\[d=10^{-3} \]
\[D = 10 \]

Answer 4

umm, d=1 mm so isn't that 1 X10 ^-3?

Answer 5

Now let's assume that the first zero intensity point lies x distance about the central line

Answer 6

Yea..I omitted the 1 ;)
Now find the value of x such that the phase difference b/w rays coming from S1 and S2 is 'pi'

Answer 7

As D >> d
We can consider the rays to be parallel while calculating path difference.
Or find the actual distance and then apply binomial..

Answer 8

Ok, from part a I managed to get
\[\lambda = 987 nm\]
The book says \[\lambda =989 nm \]so we'll go with that