## Uncertainty Problem Help [ENDORSED]

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

Michael Lonsway 3O
Posts: 43
Joined: Wed Sep 21, 2016 2:57 pm

### Uncertainty Problem Help

In the fall workbook Fall 2015 quiz prep question 3 asks: Find the uncertainty in the position of a marble of mass 1.5g given that its speed is known to within + or - 0.55m/s. I used the uncertainty equation delta x= h/m*delta v and made sure to convert mass to kg and use 1.1 m/sec speed. I got a different answer from the answer key and wondering where I went wrong.

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### Re: Uncertainty Problem Help

Michael Lonsway 3O
Posts: 43
Joined: Wed Sep 21, 2016 2:57 pm

### Re: Uncertainty Problem Help

Find the uncertainty in the position of a marble of mass 1.5g given that its speed is known to within +/- 0.55 m/s. Answer: Delta x= 3.2E-32m

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### Re: Uncertainty Problem Help  [ENDORSED]

We're given a mass of 0.0015 kg and uncertainty in speed 1.1 m/s (since it's 0.55 m/s both directions) The Heisenberg Uncertainty Principle in its mathematical form states that

$\Delta x\Delta p\geq h/(4*pi)$.

Note that p, momentum, is equal to mass times speed:

$p=mv$

This means that (uncertainty in position)(uncertainty in momentum) has to be greater than or equal to Planck's constant divided by 4pi. We're given the uncertainty in speed, and since momentum is just mass times speed, we're indirectly given the uncertainty in momentum. All that's left is to solve for the uncertainty in position:

$\Delta x\geq h/((4*pi)(\Delta (mv)))$

Plugging in 6.626 e-34 J*s for Planck's constant and (0.0015 kg)(1.1 m/s) for the uncertainty in momentum, we get that the uncertainty in position must be greater than or equal to 3.2e-32m.

Hope this helps!

Michael Lonsway 3O
Posts: 43
Joined: Wed Sep 21, 2016 2:57 pm

### Re: Uncertainty Problem Help

Thanks for the help! I got the wrong answer before since I forget to include 4pi when finding delta x.