Quantum Tunneling: Estimating Probability

[fredrick08]

Homework Statement

A 10eV electron is incident on a potential barrier of height 25eV and width 1nm. Estimate (order of magnitude) the probability that the electron will tunnel through the barrier, repeat your calculations for a barrier of 01.nm

Homework Equations

T=16(E/V)(1-(E/V))exp(-2$$\alpha$$a)
$$\alpha$$=$$\sqrt{}(2m(V-E))$$/$$\hbar$$

The Attempt at a Solution

E=10eV=1.6x10^-18J, V=25eV=4x10^-18J

$$\alpha$$=$$\sqrt{}(2*9.1x10^-31(4x10^-18-1.6x10^-18))$$/6.62x10^-34=3.157x10^9

T=3.84exp(-2*3.157x10^9*1x10^-9)=7x10^-3?

the answer is meant to be 9.2x10^-9 or 4.95x10^-13? sorry, my book says 4.95 and the lecturers notes say 9.2... doesn't matter, coz I am way way off...

please can someone help me where i am going wrong?

 

[fredrick08]

sorry about the latex the x is multiply

 

[fredrick08]

please anyone?

 

[Matterwave]

Well, the only thing I see is that instead of hbar you used h in your calculations. hbar is a factor of 2pi smaller than h.

 

[fredrick08]

omg oops, thanks

 

[fredrick08]

still have wrong answer, anyone know y?