posted by Olivia on .
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
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. :-)
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 ?