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Homework Statement
In a simple model for a radioactive nucleus, an alpha particle (m = 6.64×10^−27kg) is trapped by a square barrier that has width 2.0*10^-15 meter and height 30.0 MeV.
What is the tunneling probability if the energy of the alpha particle is 18.0MeV below the top of the barrier?
E = 18 MeV
U = 30 MeV
m = 6.64*10^-27 kg
L = 2.0*10^-15 m
ћ = 1.055*10^-34 Js
Homework Equations
[/B]
Probability of Tunneling
The Attempt at a Solution
G = 16(18/30)(1-(18/30)) = 3.84
U - E = 12*10^6 eV = 1.92*10^-12 J
κ = sqrt(2 * 6.64*10^-27 * 1.92*10^-12) / 1.055*10^-34
= 1.51*10^15 m^-1
L = 2*10^-15 m
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e^(-2κL) = e^(-2 * 1.51*10^15 * 2*10^-15) = .0023
T = G * .0023 = 3.84 * .0023
= 9.0*10^-3
I've tried solving this problem numerous times and always end up with the same value listed above. Any observation on what went wrong would be appreciated. Thanks in advance.