Quantum Physics

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A proton is confined in an atomic nucleus of size 2 fm. Determine the fundamental limit on
the uncertainty of any prediction for the measurement of the momentum of the proton in the
nucleus.

  • Quantum Physics -

    The uncertainty in proton location is
    deltax = +/- 1 fm = 10^-15 m

    The uncertainty in x-momentum is
    deltaPx = (h/4pi)/deltax = 5*10^-20 kg m/s

    where h is Planck's constant.

    Your book may eliminate the 1/(4 pi) factor. It depends upon how the uncertainty is defined. The h/4 pi value is the product of standard deviations.

    Remember that there are uncertainties in three directions of momentum. The total momentum uncertainty is a factor of sqrt3 higher.

    I would not be surprised if your book's answer is up to a factor of ten different.

    No wonder they call it the uncertainty principle. :-)

  • Quantum Physics -

    I don't understand why you've used 4 pi in your answer, i assume your rearranged the uncertainty principle equation for delta Px, but isnt the reduced plancks constant h/ 2pi instead of 4pi ?

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