How Do You Calculate Electron Tunneling Probability Through a Barrier?

AI Thread Summary
To calculate the electron tunneling probability through a barrier, the relevant equations involve the transmission probability (T) and the wave vector (k). The barrier height is 2.386 eV, the electron energy is 0.201 eV, and the barrier width is 0.383 nm. A common error in calculations is not converting electron volts to joules, which requires multiplying by the charge of an electron (1.6 x 10^-19 C). The issue was resolved by correctly converting the energies to their potential equivalents before applying the equations.
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Homework Statement



Electrons with energies of 0.201 eV are incident on a barrier 2.386 eV high and 0.383 nm wide. Find the probability for these electrons to penetrate the barrier.

Homework Equations


Note: h = h-bar

k=Sqrt[2*m (V - E)]/h

T = (1 + (V^2 (Sinh[k*L]^2))/(4*R (V - R)))^-1

where
T= transmission probability
V= potential of the barrier
E= energy of the electrons
m- mass of electrons = 9.11*10^-31
h= (4.14*10^-15)/(2*pi)
L=.383*10^-9 m

The Attempt at a Solution



I've been using the equations for k and T found both in my textbook and on wikipedia and plugging them into mathematica, but they're both giving me wrong answers. Can anyone see what's wrong?
 
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Figured it out! I had to multiply each energy by e to make it a potential. So 2.386 eV becomes (2.386*(1.6*10^-19)) V and same for the other
 
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