## Post Module #18

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

Ashley Chipoletti 1I
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Joined: Fri Sep 29, 2017 7:04 am

### Post Module #18

Can someone help me solve this?

The hydrogen atom has a radius of approximately 0.05 nm. Assume that we know the position of an electron to an accuracy of 1% of the hydrogen radius, calculate the uncertainty in the speed of the electron using the Heisenberg uncertain principle.

Sean Monji 2B
Posts: 66
Joined: Fri Sep 29, 2017 7:06 am

### Re: Post Module #18

So we know the equation for uncertainty: ΔpΔx >= h/4π
Given a distance (Δx) and Δp = m * Δv (since velocity is the only thing that is uncertain about a momentum, mass is known) we can derive
1. Δv >= h/( 4π * Δx * m)
2. The Δx of an electron is said to be within 1% of .05 nm, thus .01 * .05 * 10^-9 m is Δx.
3. Plug in variables and solve: 6.626 * 10^-34 / (4π * 5.0 * 10^-13 * 9.109×10^-31)
4. Should give answer in Δv or uncertainty in velocity (m/s)
Last edited by Sean Monji 2B on Wed Nov 08, 2017 11:57 pm, edited 2 times in total.

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