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Particle velocity

  1. Feb 2, 2016 #1
    1. The problem statement, all variables and given/known data
    To what velocity would an electron (neutron) have to be slowed down, if its wavelength
    is to be I meter? Are matter waves of macroscopic dimensions a real possibility?

    2. Relevant equations

    I have assumed this could apply to pretty much any free particle of mass m, and is an introductory question only in nature.

    3. The attempt at a solution

    I have added the units below

    I took ##p=\frac{h}{\lambda}##, with ##\lambda=1m##, so that in general for particles, ##v = \frac{h}{m} = \frac{6.626 \times 10^{-34} J.s} {1m \times 9.1 \times 10^{-31}kg} = 7.28 \times 10^{-4} m.s^{-2}##?

    For the 2nd part of the question, it seems to me that the velocity is unrealistically slow for a free particle, and would be more so for those with higher mass. I find the 2nd part of the question a little ambiguous, but assuming they are referring to wavelengths of the order of 1m, it would seem from this that waves of macroscopic dimensions are unlikely?
     
    Last edited: Feb 2, 2016
  2. jcsd
  3. Feb 2, 2016 #2

    mfb

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    Your calculations are missing units.
    Well, depends on "macroscopically". Double-slit experiments with electrons, atoms and even small molecules have been performed. Bose-Einstein condensates allow to reach even lower energies, with wavelengths of millimeters.
     
  4. Feb 2, 2016 #3
    I had read about that, but supposed that for this question they wanted a reply based on the velocity I found; I really can't read much into that velocity myself. I wonderede about quantisation of energy, so used ##\Delta E = h \nu = \frac{hv}{\lambda} = 4.8 \times 10^{-37}J = 3 \times10^{-18} eV ## - this looks too low to me, wouldn't there be a minimum energy ?
     
  5. Feb 2, 2016 #4

    mfb

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    There is no minimal energy - unless you constrain the spread of the particle (e.g. to 1 meter).
    Be careful with the energy calculation here: for massive particles, the product of frequency and wavelength is not the speed of the particle. You need a different way to calculate it.
     
  6. Feb 2, 2016 #5
    Thanks mfb, point to remember.

    Firstly, is my velocity calculation OK?

    In the absence of any known potential, we can use the KE, where ##T=\frac{1}{2}mv^2 = 5.03 \times 10^{-38} J = 3.15 \times 10^{-19} eV## ? Still seems very low?

    On a side point - for a bound particle (eg electron in an atom) - then there would be a minimum energy corresponding to the lowest energy level?
     
  7. Feb 2, 2016 #6

    mfb

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    Should be m/s, but apart from that it looks fine.
    Well, it is very low.
    Sure. On the other hand, the zero is a bit arbitrary for the potential. But you have a minimal kinetic energy.
     
  8. Feb 2, 2016 #7
    Oops on the m/s.
    I was expecting to find the energy of the order of 1eV, if an electron got knocked out of a ground state orbital for example, wouldn't it have at least that amount of energy? I'm wondering if the value I got is reasonable (given that we are using more classical physics)?
     
  9. Feb 3, 2016 #8

    mfb

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    Well, typically electrons have way shorter wavelengths - that's what the calculation is showing.
     
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