Solving Potential Barrier Problems with Electron Beams

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In summary, the conversation is about a person seeking help with problems involving potential barriers and electron beams. They have attempted to find the fraction of the incident beam that is reflected, but have not been successful. They are also unsure of how to solve for the probability of penetrating a barrier with different thickness and determining the minimum barrier thickness for no reflection. They are asking for guidance on how to solve these problems.
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jlucas134
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New some help with some problems. I have tried them an listed what I have done so far...

1. A beam of electrons is sent along the x-axis from - with kinetic energy E=7.5eV. The beam encounters a potential barrier of height V'=1eV and width 2a=1.2nm.
What fraction of the incident beam is reflected? [Hint: Assume E>>V0]
I found k and q and from these found |R|^2, but have had no success in getting the correct answer. Am I supposed to do something after I find |R|^2?

2. Suppose a wave function within a barrier is approximately proportional to e-kx. The
probability that a particle will penetrate a barrier of thickness 2a is 0.010. What is the
probability of penetrating a barrier that is twice as thick?
Not even sure where to start here... I know that my thickness will now be 4a, but what now?

3. Suppose electrons with E= 10.0 eV approach a potential barrier of height 2.0 eV.
a. Suppose electrons with E= 10.0 eV approach a potential barrier of height 2.0 eV. in nanometers

b. For what minimum barrier thickness is there no reflection? in nanometers
Not sure where to start. I think i need to solve for 2aq=n*pi for a and for b where n*pi/2.

I am not really looking for the answers, but how to solve them as there is not much help in the text.

Thanks in advance.
 
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  • #2
Can you show us your work on question 1?
 

1. What is a potential barrier?

A potential barrier is a type of energy barrier that prevents particles or molecules from moving freely through a medium. It can be created by various factors such as electric fields, chemical reactions, or physical barriers.

2. How do potential barriers affect the movement of particles?

Potential barriers can either hinder or facilitate the movement of particles. In some cases, they can completely block the movement of particles, while in others, they can act as a catalyst or aid in the movement of particles.

3. What are the different types of potential barriers?

There are several types of potential barriers, including energy barriers, diffusion barriers, and electrostatic barriers. These barriers can be found in various systems, such as biological cells, electronic devices, and chemical reactions.

4. Can potential barriers be overcome?

Yes, potential barriers can be overcome by providing enough energy to the particles. This energy can be in the form of heat, light, or other external forces. Once the potential barrier is overcome, particles can move through the barrier with ease.

5. How do scientists study potential barriers?

Scientists use various techniques such as mathematical modeling, experiments, and simulations to study potential barriers. These methods allow them to understand the behavior of particles and molecules in different environments and how potential barriers affect their movement.

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