Alice in quantumland

1. Feb 25, 2004

carmen electron

This was one of the bonus questions on my homework. Teacher says whoever gets it right, consider yourself a god or goddess. Can anyone help me solve this?

Calculate the lowest possible energy for an electron confined in a cube of sides equal to 10pm, and a cube of sides equal to 1fm. The latter cube is about the size of a nucleus. What do your energies say about the chance of an electron being inside the nucleus? *Hint: Assuming that the uncertainty in the position of the electron is the length of a side of a cube, find the change in Energy (triangle E is symbol) for each cube.

2. Feb 25, 2004

From the appearance of $$\Delta E$$ I assume you have been given the uncertainty principles for energy and time and for momentum and length. To use the E,t one, you have to get a $$\Delta t$$ out of the box side length, and I suggest you allow your electron to have a maximum speed of c, so the time it would spend in crossing the box would be ...? And the $$\Delta E$$ for that $$\Delta t$$ would be...?