Finding the Optimal Distance for Electron Tunneling in Gold

In summary, the work function of gold is 5.1 eV and the transmission probability for an electron to cross from one piece of gold to another at a distance L is given by T= Ge^(-2KL). To achieve a transmission probability of T≈ 10-3, the value of L must be (c) 0.1 nm, assuming G = 1 and using K=sqrt(2m/h^2 * (U-E)) with U-E = 5.1 eV. However, without showing the work done, it is difficult to identify any potential errors.
  • #1
LisaMG
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Homework Statement


The work function (energy needed to remove an electron) of gold is 5.1 eV. Two pieces of gold (at the same potential) are separated by a distance L.

For what value of L will the transmission probability for an electron to cross from one to the other be T≈ 10-3? Assume that G = 1 in the formula for the tunneling probability.

fig14.gif
(a) L = 0.001 nm
(b) L = 0.02 nm
(c) L = 0.1 nm
(d) L = 0.3 nm
(e) L = 4 nm

Homework Equations


T= Ge^(-2KL)
K=sqrt(2m/h^2 * (U-E))

The Attempt at a Solution


I have my final tomorrow, this is a practice exam. I tried to solve for K using 5.1eV for (U-E) and then solve for L but I can't figure it out.
 
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  • #2
LisaMG said:
I tried to solve for K using 5.1eV for (U-E) and then solve for L but I can't figure it out.
The approach is good, so unless you show your work there is no way to tell what went wrong.
 

1. What is Quantum Physics Tunneling?

Quantum Physics Tunneling, also known as tunneling or quantum tunneling, is a phenomenon in which a particle can pass through a potential barrier that it does not have enough energy to overcome. This is a result of the probabilistic nature of quantum mechanics, where particles can exist in multiple states at once.

2. How does Quantum Physics Tunneling occur?

Quantum tunneling occurs when a particle approaches a potential barrier with a lower energy than the barrier itself. According to quantum mechanics, there is a small but finite probability that the particle will pass through the barrier and appear on the other side. This is due to the wave-like nature of particles and the uncertainty principle.

3. What are the applications of Quantum Physics Tunneling?

Quantum tunneling has many applications in modern technology, such as in scanning tunneling microscopes, which use tunneling to image and manipulate individual atoms. It is also used in flash memory devices, where electrons tunnel through a barrier to store data. In nuclear fusion reactions, tunneling helps to overcome the repulsive barrier between atomic nuclei.

4. Can Quantum Physics Tunneling violate the laws of classical physics?

No, quantum tunneling does not violate the laws of classical physics. It is a phenomenon that is only observed at the quantum level and is consistent with the principles of quantum mechanics. At the macroscopic level, the effects of tunneling are too small to be noticeable.

5. How does temperature affect Quantum Physics Tunneling?

Temperature plays a significant role in quantum tunneling. As the temperature increases, the energy of particles increases, making it more likely for them to overcome potential barriers without tunneling. This is why quantum tunneling is more prevalent at very low temperatures, such as in superconductors, where particles have very little thermal energy.

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