Posted by **Olivia** on Wednesday, May 18, 2011 at 6:52am.

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 -
**drwls**, Wednesday, May 18, 2011 at 7:16am
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 -
**Simon**, Monday, May 23, 2011 at 9:27am
I dont 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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