Question 26 Sapling

[Brandon Gruender 3F]

On the Sapling HW, it asks

What is the minimum uncertainty in an electron's velocity (Δvmin) if the position is known within 13 Å.

How do I solve this?

[Charlene D 3H]

Hi!
You can convert the uncertainty of position to meters, then plug that value in for delta x in the Heisenberg Indeterminacy equation. From there you can solve for delta V using the mass of an electron.
Let me know if you need any more clarification!

[Eliana Witham 2H]

Adding on to Charlene's answer, you can use the equation (uncertainty in momentum)=(mass)(uncertainty in velocity) to substitute for uncertainty in momentum in Heisenberg's Indeterminacy Equation. Therefore, you can get the final answer using only one equation.

[Namratha Gujje]

In order to solve this problem, you would have to use Heisenberg's uncertainty equation which is. You would need to rearrange this equation so that you are solving for the uncertainty in the electrons velocity. This would just mean that v is greater than h/(4pi)(mass)(Position). Mass of an electron is a constant that can be found on the equation sheet we got for the midterm. Also make sure to convert angstroms to meters.

[jasmineculilap_3F]

You can use heisenberg's uncertainty principle where ΔxΔp >= h/4π. Δp = mΔv, so you can substitute that in and rearrange the equation for Δv which becomes Δv = h/(4πmΔx). Then, you can just plug in electron mass and Δx which is given to you.

[Melanie Lin 3E]

Hi Brandon!
There will be two equations that you have to utilize that can be found on Lavelle's equation sheet. You use ΔxΔp >= h/4π to find Δp with the Δx given to you (13 Å, which you should convert to meters). With the Δp solved for, you can find the uncertainty in velocity using the equation Δp = mΔv. Hope this helps!