# Tunneling effect problem

## Homework Statement

We consider a simple model of alpha decay. Imagine an alpha particle moving around inside a nucleus. When the alpha bounces against the surface of the nucleus, it meets a barrier caused by the attractive nuclear force. The dimensions of this barrier vary alot from one nucleus to another, but as representative numbers you can assume that the barriers width is 35 fm and the average barrier height U0 x E = 5MeV. Find the probability that an alpha particle hitting the nuclear surface will escape. Given that the alpha hits the nuclear surface about 5x10^21 times per sec, what is the probability that it will escape in a day?

## Homework Equations

Transmission probability is given by:
T(E) = {1+1/4[U^2/E(U-E)]sinh^2ALPHA*L}^-1
ALPHA = sqrt(2m(U-E))/h.bar

There are 86400s in a day: 4.32E36 alpha-hit

## The Attempt at a Solution

I tried using E = (h.bar^2 x k^2)/2m but then it gives me a really really weird answer. Can anyone help me crack this problem?