Question from the textbook

[Tala Ayoub 1H]

A proton is accelerated in a cyclotron to a very high speed that is known to within 3.0x10^2 km.s^-1. What is the minimum uncertainty in its position?

How would I solve this question?

[Nancy Li 1C]

We are given that ∆v = 3.0 x 10^2 km/s so I would first convert this to m/s (3.0 x 10^5 m/s). Using Heisenberg's Uncertainty Equation, we have that ∆x∆p >= h/4pi. ∆p = m∆v so using the mass of a proton we find that ∆p = 1.67 x 10^-27 * 3.0 x 10^5 = 5.01 x 10^-22. Plugging this back into Heisenberg's Equation, we are able to solve for ∆x for a final answer of 1.05 x 10^-13 m.

[Sidney Shah 3H]

The value given, 3.0x10^2 km.s^-1, is equal to delta v, which you can use to solve for delta p or momentum by multiplying by the mass of a proton. Then you can plug this value into the Heisenberg Indeterminacy Equation!

[Amanda Tran 1D]

The problem gives you the value for , and is asking you to solve for . Using Heisenberg's uncertainty principle, we know that , which can also be written as . We want to solve for , so we can rearrange this to look like: . From here, you can plug in the value for delta V which you were given, and then Planck's constant and the mass of the proton.

[Harrington Bubb3A]

If you know the velocity, then solve for the change in x by dividing the right hand of the equation by the velocity and you get the displacement. Make sure to convert to SI units!