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## Homework Statement

A proton's energy is 1.30 MeV below the top of a 14.0 fm-wide energy barrier, What is the probability that the proton will tunnel through the barrier?

## Homework Equations

[itex]η=\frac{\hbar}{\sqrt{2m(U_{0}-E)}}[/itex]

[itex]P_{tunneling}=e^{\frac{-2w}{η}}[/itex]

## The Attempt at a Solution

I have got a probability of using the following method. Just want to check if it is the wright answer.

[itex]w=1.4*10^{-14}[/itex] ∴ [itex]2w=2.8*10^{-14}[/itex]

[itex]m_{proton}≈ 1.67*10^{-27}[/itex] ∴ [itex]2m_{proton}≈ 3.35*10^{-27}[/itex]

[itex](U_{0}-E)=1.3MeV≈2.08*10^{-10}J[/itex]

[itex]{\sqrt{2m(U_{0}-E)}}=8.35*10^{-19}[/itex]

[itex]η=\frac{\hbar}{\sqrt{2m(U_{0}-E)}}=1.26*10^{-16}[/itex]

[itex]P_{tunneling}=e^{\frac{-2.8*10^{-14}}{1.26*10^{-16}}}[/itex]

[itex]P_{tunneling}≈e^{-221.63}[/itex]

[itex]P_{tunneling}≈5.6^{-97}[/itex]

The answer is 0% chance of tunneling ( is this wright or have I made a mistake somewhere?)

Thanks in advance

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