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j2dabizo
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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