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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 a lot 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?