00:01
Hi there, so for this problem, we're told that a proton is traveling with a speed that is given, and that speed is equal to 8 .660 plus or minus 0 .013 times 10 to the 5 meters per second.
00:27
So the question is, with what maximum precision can its position be ascertain? with that said, we know that we need to obtain the uncertainty on the position.
00:48
And for that, we use the eisenberg absurdity principle that states that the period between the position and the momentum is equal, well, its minimum value can be just plans constant divided by, 4 times pi.
01:04
Now, the change in the position, the uncertainty on the position can be written as the mass of the particle because it is not changing, times the absurdity on the velocity.
01:17
And that uncertainty is given in here because this is the initial value plus or minus the uncertainty.
01:23
So the uncertainty in this case, for the speed is 0 .013 times 10 to the 5 meters per second.
01:32
Now, if we substitute that in here and then solve for the uncertainty on the position, that will be just simply equal to 4 times pi times the mass of a proton times the uncertainty on the speed...