Barrier Tunneling: Proton Transmission Coefficient

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A user encountered difficulties calculating the transmission coefficient T for a 3.0 MeV proton incident on a 10 MeV potential barrier. They initially applied the formula T=e^(-2bL) and calculated b using the given parameters, resulting in an extremely low transmission coefficient. Upon posting, they realized their mistake in the calculations. The correct transmission coefficient, as stated in the book, is 9.02*10^-6. The discussion highlights the importance of careful calculation in quantum mechanics problems.
Kazza_765
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I can't work out what I am doing wrong in this question. Anyways, here it is:
A 3.0 MeV proton is incident on a potential energy barrier of thickness 10fm and height 10 MeV. What is the transmission coefficient T.
And here is what I have tried:
T=e^(-2bL)
b=\sqrt{\frac{8\pi^2m(U_b-E)}{h^2}}
b=\sqrt{\frac{8\pi^2(1.673*10^-27)\frac{10*10^6 - 3*10^6}{1.602*10^-19}}{(6.626*10^-34)^2}}
b=3.626*10^33
This gives me a transmission coeffecient of approximately 0, and the answer given in the book is 9.02*10^-6. Your help on this is much appreciated.
 
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Never mind, as soon as I posted it and saw my equation in front of me I worked it out. Silly mistake.
 
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