Question

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.

Answer 1

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. :-)

Answer 2

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 ?