Minimum energy needed for a positrons to tunnel

In summary, the question discusses the minimum kinetic energy required for positrons to penetrate a 10eV, 1nm barrier. The equations used to solve this problem involve p_T = e^(-2*a*L) and a = (sqrt(2m(V_0-E))/hbar. The solution involves finding the point at which one positron will pass on average.
  • #1
ElectricEel1
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Homework Statement


10^12 positrons of the same kinetic energy are incident on 10eV, 1nm barrier. What is the minimum kinetic energy the positrons need before any of them can penetrate the barrier?

Homework Equations


p_T = e^(-2*a*L)
a = (sqrt(2m(V_0-E))/hbar

The Attempt at a Solution



For other problems I've plugged numbers into these equations to find non zero probabilities but this time I'm not sure how to solve it. I tried setting p_T to zero and rearranging for E but that just ended up as V_0=E.
 
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  • #2
Theoretically, they can pass the barrier regardless of their energy. It is just that the probability will be vanishingly small.

What I would guess the problem wants you to do is to figure out when on average one positron will pass.

Can you clarify the question?
 

FAQ: Minimum energy needed for a positrons to tunnel

1. What is the minimum energy needed for a positron to tunnel?

The minimum energy needed for a positron to tunnel is known as the tunneling energy or the tunneling barrier. It is the energy required for a particle to pass through a potential barrier, such as an energy barrier created by a potential well.

2. How is the minimum energy for positron tunneling calculated?

The minimum energy for positron tunneling is calculated using the Schrodinger equation, which describes the wave-like behavior of particles. The equation takes into account the potential barrier, the mass and energy of the particle, and the particle's wave function.

3. Can the minimum energy for positron tunneling be measured experimentally?

Yes, the minimum energy for positron tunneling can be measured experimentally using techniques such as scanning tunneling microscopy or tunneling spectroscopy. These methods involve measuring the electrical current between a probe and a sample, and the energy required for the current to pass through a potential barrier is determined.

4. How does the minimum energy for positron tunneling differ from the minimum energy for electron tunneling?

The minimum energy for positron tunneling is typically higher than the minimum energy for electron tunneling. This is because positrons have a positive charge, while electrons have a negative charge. The positive charge of the positron interacts with the electric field of the potential barrier, making it more difficult to tunnel through compared to an electron.

5. What factors affect the minimum energy for positron tunneling?

The minimum energy for positron tunneling can be affected by several factors, such as the thickness and height of the potential barrier, the energy and mass of the positron, and the properties of the material the positron is tunneling through. Additionally, the temperature and pressure of the environment can also impact the minimum energy for positron tunneling.

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