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Homework Help: De Broglie's Wavelength (matter wave)

  1. Jul 27, 2010 #1
    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?
    Please help...

    Thank you in advance
     
  2. jcsd
  3. Jul 27, 2010 #2

    vela

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    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.
     
  4. Jul 28, 2010 #3
    I see :smile:.

    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
     
  5. Jul 28, 2010 #4
    Anyone? please.
     
  6. Jul 29, 2010 #5

    vela

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    What does the addition of more slits do to the interference pattern?
     
  7. Jul 30, 2010 #6
    :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)...

    sorry about my silliness..
     
  8. Jul 30, 2010 #7

    vela

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    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.
     
  9. Jul 30, 2010 #8
    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?

    Again, thanks you for your time & patience in advance. :smile:
     
  10. Jul 30, 2010 #9

    vela

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    Yes, "cold" means "slow."
     
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