Homework Problem 1.43

[sboutros2B]

Hello everyone! I was wondering if someone can give me a brief overview on how to approach this problem.

what is the minimum uncertainty in the speed of an electron confined to within a lead atom of diameter 350. pm? Model the atom as a one dimensional box with a length equal to the diameter of the actual atom.

(mainly need help with modeling the atom)

[Chelsey_Schaum1H]

Hey!
So this question is regarding the Heisenberg uncertainty principle which is
(Delta x)(delta p)= h/4pi
You are given the uncertainty in position (delta x) as 350 pm. You are asked to find the uncertainty in speed, or velocity, but first you have to find the uncertainty in momentum (delta p).
First step is to convert 350 pm to m, which is 350x 10^-12.
Then solve the equation for delta p. So h/( (4pi)(delta x))= delta p
Once you have delta p you can then solve for delta v (speed) by using the equation delta p= mass x delta v
When you solve the equation for delta V that is your final answer

The modeling of the atom part I wouldn't worry much about. It's talking about the box model of an atom which professor lavelle said he will not be testing us on or really teaching it to us at this time.