Tunneling with an alpha particle

[Differentiate1]

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

---------------------------------------------------------------------------------------

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.

 

[Orodruin]

E is defined as being 18 MeV below the barrier, not as being 18 MeV. This does not matter for G but it does for kappa.

 

[Differentiate1]

Would that simply mean for kappa, instead of U - E, since it's below the barrier, it would be E - U?
My book defines U - E as being the additional KE needed to climb over the barrier.

Actually, that won't work algebraically since the numerator will be the square root of a negative value.
I am uncertain about this--maybe if the particle tunnels below, it means U - (-E)?

 

[Orodruin]

No, it means that U-E is 18 MeV.

 

[Differentiate1]

Can you please explain the concept behind why that's the case?

 

[Orodruin]

Can you please explain the concept behind why that's the case?

Because this is what the problem states:

the energy of the alpha particle is 18.0MeV below the top of the barrier

 

[Differentiate1]

Thank you for your assistance!