## 1B.26

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

Yun Su Choi 3G
Posts: 87
Joined: Wed Sep 30, 2020 10:09 pm

### 1B.26

I know this problem wasn't assigned, but if anyone did it, I'd like to check answers.

What is the minimum uncertainty in the position of a hydrogen atom in a particle accelerator given that its speed is known to within +- 5.0m/s?
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Halle Villalobos 3E
Posts: 85
Joined: Wed Sep 30, 2020 9:52 pm

### Re: 1B.26

Hi! First we rearrange Heisenberg's indeterminacy equation to $\Delta x \geq \frac{h}{4pi*m \Delta v}$. Plugging in our known values gives us $\Delta x \geq \frac {h}{(4pi)(1.68*10^{-27})(10)}$ which results in a minimum uncertainty in position of 3.1 nm. I hope this helps!

Olivia Yang 3J
Posts: 90
Joined: Wed Sep 30, 2020 10:00 pm
Been upvoted: 2 times

### Re: 1B.26

So the velocity uncertainty is 10? What if the value was given as 10 +- 0.04? What would be the velocity uncertainty then?

rhettfarmer-3H
Posts: 96
Joined: Wed Sep 30, 2020 9:59 pm

### Re: 1B.26

Olivia Yang 1D wrote:So the velocity uncertainty is 10? What if the value was given as 10 +- 0.04? What would be the velocity uncertainty then?

If the values was 10+- .04 then our uncertainty would be the difference in the .04 *2 (for both postive and negative). Hence the uncertainty in the velocity would be .08. The initial velocity has nothing to do with uncertainty the uncertainty is just the change in velocity due to error in-measurement