Uncertainty in velocity of proton in hydrogen atom

[Jeffrey Hablewitz 2I]

In lecture 9, Dr. Lavelle works an example which shows that the uncertainty in the velocity of an electron contained in the nucleus of an atom exceeds the speed of light. Using this reasoning, I attempted to calculate the uncertainty in the velocity of a proton, which we know is contained in the nucleus of the atom. I replaced the mass of an electron with the mass of a proton in Dr. Lavelle's calculation but the result I got is an uncertainty of 1.8*10^7 m/s. This seems really high to me. What am I doing wrong?

[JoshMoore2B]

This caught my eye, so I decided to take a look.

Using the values given to us from Wednesday's lecture, and using the indeterminacy equation, we have something like this:

deltaV >= h/(4pi * deltaX * Mass_proton)

or

deltaV >= (6.63x10^-34 J*s)/((4pi)(1.7x10^-15m)(1.67x10^-27kg)

which, when worked out mathematically, gives the same number as you calculated: roughly 1.9x10^7 m/s.

Using the logic Dr. Lavelle gave during the lecture about the electron, this is an acceptable answer. The uncertainty for the electron was on the degree of 10^10, which is higher than the speed of light (10^8). This means that, physically, an electron could not be confined to the nucleus of an atom, because then it could, through its uncertainty, be conceivably moving faster than light. However, the uncertainty of the proton's velocity being only on the degree of 10^7 is perfectly okay, because although this number may seem very high, it doesn't disobey the laws of physics surrounding the speed of light. Thus, a proton can be confined to the space of a hydrogen atom.

In other words, it doesn't seem as though you've done anything wrong. Instead, it seems that the laws of the smalls (quantum particles and their friends) may be a bit confusing or startling - which is okay! They're confusing for everyone.

[Jeffrey Hablewitz 2I]

Thanks for the response. I also realized that the nucleus of a hydrogen atom is usually only one proton, so the measurement Dr. Lavelle used was the diameter of a proton. This might have contributed to the really high uncertainty.