## Textbook 1B 25

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

Nicole Huang 3F
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### Textbook 1B 25

For Textbook Question 1B.25, how do would you go about finding the speed of the electron? I understand that the end goal is finding the v from change in momentum, but how do we find change in position in the Heisenberg Equation? Is it from the diameter of the lead atom?
Any explanation may help, thanks!

Pranav Daggubati 3C
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### Re: Textbook 1B 25

Correct, you would use the diameter of the atom as $\Delta x$ because that is the boundary of the electron is space.

KatarinaReid_3H
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### Re: Textbook 1B 25

First, use the equation delta p is greater or equal to (h/(4pi(delta x)).
Delta x = 350e-12 meters. Now solve for p(momentum). Once you have p=1.49e-24, then set that equal to mass x velocity. You have the mass of an electron, so you just need to solve for velocity which is 1.63e5 m/s.

EmilyGillen_1A
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### Re: Textbook 1B 25

For this problem I follow the logic and step/process, but I am confused as to why the delta(v) is only 5 instead of 10. In the equation it says that the speed is 5.0 m/s + or - 5, so wouldn't that mean the uncertainty is 10 not 5? (5 for +5 and 5 for -5)
I guess I am confused because I thought in lecture he mentioned making sure to count both side of the given uncertainty, but putting 10 in here would give you the wrong answer.

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### Re: Textbook 1B 25

EmilyGillen_1A wrote:For this problem I follow the logic and step/process, but I am confused as to why the delta(v) is only 5 instead of 10. In the equation it says that the speed is 5.0 m/s + or - 5, so wouldn't that mean the uncertainty is 10 not 5? (5 for +5 and 5 for -5)
I guess I am confused because I thought in lecture he mentioned making sure to count both side of the given uncertainty, but putting 10 in here would give you the wrong answer.

I think you're referring to 1B 27, but yes, the uncertainty in velocity would be 10 because you multiply by two when there’s a ± because that represents the range of values that the speed could be. I believe that there’s an error in the answer key. You can find the correct solution here. https://lavelle.chem.ucla.edu/wp-conten ... rs_7Ed.pdf