Barrier and Tunneling Problem

[j2dabizo]

Homework Statement

A 1.1 eV electron has a 10-4 probability of tunneling through a 2.4 eV potential barrier. What is the probability of a 1.1 eV proton tunneling through the same barrier

Homework Equations

eq 1) T= [1 + V₀² sinh²(kL)/4E(V₀-E)]^-1

or if (kL)>>1 we use eq 2) T= 16(E/V₀(1-E/V₀)e^-2kL


k= (2m(V₀-E)^1/2/hbar

The Attempt at a Solution

Solving for k.
we know m of electron= 5.11E5 ev
Vo = 2.4
E= 1.1
hbar = 6.5281E-16 ev*s...

so solve for k of electron we get 1.7512E18 s^-1, need it in terms of m^-1, so we divide by 3.0E8m/s = 5.8373E9 m^-1

solve for L in equation 2 t= (7.333)(0.5417)e^{-1.1675E10m-1}(L)...
L= 3.9392E-10m

now i have found L,

nned to find k of the proton so..

k=[2(938.27E6ev)(1.3ev)]^1/2/6.5821E-16ev*s = then divide by 3.0E8 m/s = 2.5013E11m^-1

so kL for proton = (205.1062)

when I plug this kL number in eq 1 or 2...once I do the e^-2(kL) or sinh(kL)² i get an error message and i can't calculate the T...

Help please this is killing me

 

[grey_earl]

That's because e^(-410) is zero for all practical purposes (i.e. experiments that could detect it today or in some ten years of time ahead).
If you really need it, e^(-410) \approx 10^(-178)