# Tunnelling probability

1. Oct 11, 2012

### Kaldanis

I'm in the process of studying for my final and I just can't solve this problem:

The work function (energy needed to remove an electron) of gold is 5.1 eV. Two pieces of gold (at the same potential) are separated by a distance L.

For what value of L will the transmission probability for an electron to cross from one to the other be T ≈ 10-3? Assume that G = 1 in the formula for the tunneling probability.

(a) L = 0.001 nm
(b) L = 0.02 nm
(c) L = 0.1 nm
(d) L = 0.3 nm
(e) L = 4

The attempt at a solution

I'm pretty sure I rearrange the tunneling equation and solve for L. Things are made easier since I'm told G=1. This means that $L = -\frac{ln(T)}{2K}$ , where $K=\sqrt{\frac{2m}{\hbar}(U_{0-E})}$. My only problem is which values do I use for U0 and E?

2. Oct 12, 2012

### PhysicsGente

E is total energy and V is potential energy. Oh, and think about the definition of the work function ;).

3. Oct 15, 2012

### Kaldanis

I'm still not having any luck with this problem. I know that I need to find the Potential Energy (U0) and total Energy. The work function is given as 5.1eV and from the picture it looks like this is the value of the PE, I think I could be wrong though. I still have no idea how to find potential and total from only the work function.

My final for quantum is tomorrow, can anyone help clear this up for me?

4. Oct 15, 2012

### Kaldanis

Nevermind, I got it. :)

5. Aug 29, 2013

### tarunnurat

How did you do it? I have my final in a few hours and it would be nice to know.