## Midterm Question

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

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Cristian Carrasco 1F
Posts: 52
Joined: Fri Sep 29, 2017 7:06 am

### Midterm Question

I know the formula to solve this but I'm confused on how to solve it ?

Find the uncertainty in the position of a marble of mass 1.5 g given that it’s speed is
known to within ± 0.55 m.s-1.

Kevin Ru 1D
Posts: 50
Joined: Thu Jul 13, 2017 3:00 am

### Re: Midterm Question

As you know, Heisenberg's uncertainty principle is: Δp x Δx ≥ h/4π

Now, the question gives us the mass of the marble as well as the uncertainty in velocity which allows us to find Δp. Since momentum is mass x velocity, you take 1.5 x 10^-3 kg (converted from grams) x 1.1 m/s (because +/-). This will give you your Δp value. Simply divide the other side of the equation by Δp and you will have solved for Δx.

Hope that helps!

Aijun Zhang 1D
Posts: 53
Joined: Tue Oct 10, 2017 7:13 am

### Re: Midterm Question

The point is that the uncertainty of velocity is 0.55 x2 = 1.1 m/s since it can be plus or minus 0.55. The range is actually larger.
momentum(p) = m * v.
uncertainty in momentum in this case = m * Δv.
so Δp = 0.55 * 2 * 1.5 * 10^-3 (you need to convert grams into standard unit kilograms)
The Heisenberg's uncertainty principle is: Δp x Δx ≥ h/4π. So the equation becomes 0.55 * 2 * 1.5 * 10^-3 * Δx ≥ h/4π.
With h and π are constants, you then can calculate Δp.
The answer is 3.2*10^-32 m.

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