Homework 1B25 Help

[AChoudhry_1L]

Can someone explain how to find the answer to this problem?

1B.25) What is the minimum uncertainty in the speed of an electron confined 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.

[Benjamin Feng 1B]

To solve this problem, you need to use Heisenberg's Equation, which is delta p * delta x >= h/(4pi), where h is a Plank's constant, delta x is the uncertainty of position, and delta p is uncertainty in momentum.

The goal of the question is to find the minimum uncertainty in speed which you can find as momentum is mass * velocity.

You can rewrite the equation as m * delta v * delta x >= h/(4pi).

You can then rearrange the equation to solve for delta v by subbing in h, m (mass of electron), and delta x (diameter of the atom).