## Uncertainty calculation

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Toru Fiberesima 1L
Posts: 63
Joined: Fri Apr 06, 2018 11:02 am

### Uncertainty calculation

If a proton is accelerated in a cyclotron to a very high speed that is known to within 3.0x10^2km*s^-1. So you know the speed, you can find out the momentum, but how do you find out the minimum uncertainty in the position.

Sarah Brecher 1I
Posts: 31
Joined: Fri Apr 06, 2018 11:02 am

### Re: Uncertainty calculation

Uncertainty in position is the Δx in the Heisenberg uncertainty equation which is ΔxΔp > h/4π. Δp is momentum, which also can be written as m*v.

Therefore, you would rewrite the equation as ΔxmΔv > h/4π and then rewrite it so that Δx is isolated (since that is what you are solving for). You are given the v, but you would need to convert into proper units, which are m/s. You can use the proton mass given on the equation sheet, as well as h. So just plug those in and you should get your answer!