How Do You Calculate Electron Tunneling Probability Through a Barrier?

In summary, the question asks for the probability for electrons with energies of 0.201 eV to penetrate a barrier 2.386 eV high and 0.383 nm wide. The equations used to solve this problem include k = Sqrt[2*m (V - E)]/h and T = (1 + (V^2 (Sinh[k*L]^2))/(4*R (V - R)))^-1. After plugging in the given values for potential, energy, mass, and h-bar, the correct solution can be found.
  • #1
dinospamoni
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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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  • #2
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
 

1. What is QM Tunneling of electrons?

QM Tunneling of electrons, also known as quantum tunneling, is a phenomenon in which particles can pass through barriers that would normally be considered impenetrable according to classical physics. In this case, electrons can "tunnel" through energy barriers that are higher than their own energy levels.

2. How does QM Tunneling of electrons occur?

QM Tunneling of electrons occurs due to the wave-like nature of particles at the quantum level. According to the Heisenberg uncertainty principle, there is always some uncertainty in the position and momentum of a particle. This allows for the possibility of a particle being able to pass through a potential barrier by "tunneling" through its wave function.

3. What are the applications of QM Tunneling of electrons?

QM Tunneling of electrons has various applications in technology, such as in the creation of tunneling diodes and scanning tunneling microscopes. It also plays a crucial role in processes like nuclear fusion and radioactive decay.

4. What factors affect the rate of QM Tunneling of electrons?

The rate of QM Tunneling of electrons is affected by the thickness and height of the energy barrier, as well as the energy levels of the particle and the barrier. The mass of the particle and the temperature also play a role in the rate of tunneling.

5. How does QM Tunneling of electrons relate to quantum mechanics?

QM Tunneling of electrons is a fundamental concept in quantum mechanics. It demonstrates the probabilistic nature of particles at the quantum level and challenges classical notions of determinism. It also plays a crucial role in understanding the behavior of particles in quantum systems and phenomena.

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