# Uncertainty Principle, Energy and Position

1. Mar 30, 2010

### MrJohnnyPrice

1. The problem statement, all variables and given/known data

Electrons in atoms are known to have energies in the range of a few eV. Show that the uncertainty principle allows electrons of this energy to be confined in a region the size of an atom (0.1 nm)

2. Relevant equations

$$\Delta$$x$$\Delta$$p $$\geq$$ h bar / 2

$$\Delta$$E$$\Delta$$t $$\geq$$ h bar / 2

3. The attempt at a solution

h bar = 6.58 x 10^-16 eV * s
$$\Delta$$x = .1 nm

I know that if there was an uncertainty relationship between Energy and displacement I could set h bar and $$\Delta$$x to the values given and show that this is possible, but I can't figure out how to find an energy position uncertainty relation.

2. Mar 31, 2010

### Feldoh

1/2mv^2 and mv look an awful lot a like...