How Do You Calculate the Barrier Width for Electron Tunneling in Gold?

In summary, we are given the work function of gold (5.1 eV) and two pieces of gold separated by a distance L. The question asks for the value of L where the transmission probability for an electron to cross from one piece to the other is approximately 10^-3. The formula for tunneling probability is given as T ≈ G*e^-2KL, where G = 1 and K = 2*pi*√((2*m)/h^2)*(Uo-E). We are given the values for m, h, and Uo, but it is unclear how to find the value for E to plug into the formula. The options are the work function minus the energy of the electron or the work
  • #1
RaoulDuke
7
0

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.

Homework Equations



T [tex]\approx[/tex] G*e-2KL
where K=2*pi*[tex]\sqrt{((2*m)/h2)*(Uo-E))}[/tex]

T: Tunneling Probability
m: Electron Mass
Uo: Potential (the work function in this case)
E: Energy of the electron
L: Length of the potential barrier to tunnel
h: Planck's constant

The Attempt at a Solution



It seems to be a simple plug and chug, but how do I find the energy to use in the (Uo-E) part in the tunneling equation?
 
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  • #2
I'm not sure if it's the work function minus the energy of the electron or the work function plus the energy of the electron.
 

FAQ: How Do You Calculate the Barrier Width for Electron Tunneling in Gold?

1. What is "tunneling with unknown energy"?

"Tunneling with unknown energy" refers to the phenomenon in quantum mechanics where a particle has a probability of passing through a potential barrier even if it does not have enough energy to overcome the barrier. This is possible because of the wave-like nature of particles at the quantum level.

2. How does tunneling with unknown energy occur?

Tunneling with unknown energy occurs when a particle encounters a potential barrier, such as an energy barrier or a physical barrier. The particle behaves as a wave and has a small probability of passing through the barrier, rather than being reflected or absorbed by it.

3. What is the significance of tunneling with unknown energy?

The significance of tunneling with unknown energy lies in its implications for quantum mechanics and our understanding of the fundamental nature of particles. It also has practical applications in fields such as electronics and nuclear physics.

4. Can tunneling with unknown energy be observed in everyday life?

No, tunneling with unknown energy is a phenomenon that occurs at the quantum level and cannot be observed in everyday life. It is only observable under controlled laboratory conditions using specialized equipment.

5. Is there any way to control or manipulate tunneling with unknown energy?

While it is not possible to control or manipulate the occurrence of tunneling with unknown energy, scientists have developed methods to enhance or suppress it in specific systems. This can be achieved through the use of different materials and designing barriers with specific properties.

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