Heisenberg uncertainty principle calculations

[Jzhang27143]

I am having some trouble understanding what to use for the uncertainties in the Heisenberg principle. My chemistry book has two problems on this principle. One asks to find the minimum uncertainty in the position of a marble of mass 1.0g given that its speed is known within +- 1.0 mm/s. The other asks to find the minimum uncertainty in the speed of an electron confined to within the diameter of 200. pm.

The book says that the uncertainty of the speed in the first problem is 2.0 mm/s and the uncertainty of position in the second problem is 200. pm. I thought that the uncertainties are 1.0 mm/s in the first problem and 100. pm since uncertainty is defined as estimate +- uncertainty. I went to other sources and found a good number that use my book's reasoning and others that use my reasoning. What do I actually use when calculating uncertainty?

 

[mfb]

It does not matter, as both methods just give a rough estimate. A proper analysis would have to take the exact shape of the distribution into account, which probably means you would need to set up some wave function and do a Fourier transformation on it. I guess you did not learn that yet, so the rough estimate is fine - and a factor of two does not matter there.