Calculating Quantum Tunneling Probability - 1.524 eV, 343 pm, 2.654 eV

In summary, the approximate transmission probability of an electron with total energy 1.524 eV through a barrier of thickness 343 pm and potential height of 2.654 eV can be calculated using the equation K = sqrt{[2m(E-V0)] / (h-bar^2)} and the formula exp(-2 *kappa *barrier thickness). The potential energy before and after the barrier does not significantly affect the transmission probability as long as it is less than 1.524 eV.
  • #1
alexis12
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Homework Statement


What is the approximate transmission probability (in %) of an electron with total energy 1.524 eV through a barrier of thickness 343 pm, and a potential height of 2.654 eV? (Does it matter what the potential energy is before and after the barrier? Not really, as long as it is <1.524 eV, so in both cases there is a traveling wave.)

Homework Equations


None given however I believe it has something to do with: http://en.wikipedia.org/wiki/Transmission_coefficient

I've managed the previous question which was about probability of transmission however it didn't deal with barrier thickness which I am not accustomed to. I can't find any literature on the subject other than the Wikipedia article I linked.

The Attempt at a Solution


No real attempt, I managed to calculate Kappa which is
K = Square root of {[2m(E-V0)] / (h-bar^2)}
 
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  • #2
Figured it out! It's exp(-2 *kappa *barrier thickness)
 

Related to Calculating Quantum Tunneling Probability - 1.524 eV, 343 pm, 2.654 eV

1. What is quantum tunneling and why is it important?

Quantum tunneling is a phenomenon in which a particle can pass through a potential barrier that would normally be impossible to overcome according to classical physics. It is important because it plays a crucial role in many physical processes, such as radioactive decay and the operation of electronic devices.

2. How is the probability of quantum tunneling calculated?

The probability of quantum tunneling is calculated using the Schrödinger equation, which describes the behavior of quantum particles. It takes into account the energy of the particle, the width of the potential barrier, and the particle's mass and position.

3. What do the values 1.524 eV, 343 pm, and 2.654 eV represent in this context?

The values 1.524 eV, 343 pm, and 2.654 eV represent the energy of the particle, the width of the potential barrier, and the total energy of the particle, respectively. These values are used in the calculation of the probability of quantum tunneling.

4. How does the probability of quantum tunneling change with different values of energy and barrier width?

The probability of quantum tunneling increases as the energy of the particle increases, and decreases as the width of the potential barrier increases. This is because higher energy particles have a greater chance of overcoming the barrier, while wider barriers make it more difficult for the particle to tunnel through.

5. Can the probability of quantum tunneling ever be 100%?

No, the probability of quantum tunneling can never be 100%. This is because there is always a chance that the particle will not tunnel through the barrier, and instead be reflected or absorbed by it. However, the probability can approach 100% for particles with very high energies and narrow barriers.

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