# De Broglie's Wavelength (matter wave)

1. Jul 27, 2010

### wavingerwin

1. The problem statement, all variables and given/known data
Parallel beam of "cold" neutrons in the x-axis, with energy 0.1eV strikes a slit system in y-z plane.

Slits are parallel to the y-axis 1 micron apart. What will be the distance between the detector at x=20m which records the highest flux of neutrons, and the closest one to it that records nearly zero flux?

2. Relevant equations
lambda = h/p
f = E/h

3. The attempt at a solution
I tried to find lambda
going with

lambda = h/p
p = gamma*m*v

v = c*(1-(K/mc2+1)-2)0.5

with K = 0.1eV = 1.602e-20 Joules
m = 1.675e-27
I found v=0... since K2/mc2 << 1

What am I doing wrong?

2. Jul 27, 2010

### vela

Staff Emeritus
The neutron has a mass of almost 1 GeV. With a kinetic energy of only 0.1 eV, it's not moving at relativistic speeds, so just use p=mv and K=1/2 mv2.

3. Jul 28, 2010

### wavingerwin

I see .

So now that I have lambda = 9.04e-11 m

Can I use the equation (n-0.5)lambda = d sin(theta)

with n = 1

and x = 20 tan(theta)

so that x is the closest distance between the central maxima and the area of nearly zero flux?

I am concerned since the problem states that the neutrons go through a "slit system" and my tutor confirmed that this means that it has multiple slits, can I still use (n-0.5)lambda = d sin(theta) which I understand is mainly used for dual-slit?

if not, what equation should I use?

Since it says that the neutrons are in a "beam", can I say that even though there are multiple slits (1 micron apart), only 2 slits are playing a part in the problem?

thank you

4. Jul 28, 2010

### wavingerwin

5. Jul 29, 2010

### vela

Staff Emeritus
What does the addition of more slits do to the interference pattern?

6. Jul 30, 2010

### wavingerwin

:shy:...It does not do anything...

I get it now that the 'slit system' is juts a diffraction grating and reading back my old notes about diffraction grating, the only difference is that now I cannot approximate sin(theta)=tan(theta)...

7. Jul 30, 2010

### vela

Staff Emeritus
The pattern does change, and it has nothing to do with the approximation sin θ≈tan θ. That only requires that θ be small.

The positions of the maxima don't change, but the peaks become narrower, more well-defined.

8. Jul 30, 2010

### wavingerwin

Thanks vela..

the last part of the question says:
If the neutron come originally from a U-235 nuclear fission reactor, in what sense are they now "cold"?

I looked at wikipedia, and found "The neutron temperature, also called the neutron energy, indicates a free neutron's kinetic energy"

My guess is the neutrons are cold in the sense that they are traveling 'slow'.

Would that be right?