Textbook 1B 25

[Nicole Huang 3F]

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]

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

[KatarinaReid_3H]

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]

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.

[Asia Yamada 2B]

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