# For proton and electron of identical energy encounter same potential

• somebody-nobody
In summary, the probability of transmission for a proton and electron encountering the same potential barrier depends on the height and length of the barrier as well as the energy of the particles. For a given barrier height and length, there exists an energy where one particle will have a transmission probability of 1 and the other will have a probability less than 1. This problem is further explained on Wikipedia, where the transmission coefficient for the case of E<V_0 is discussed. By choosing k_1 such that \sin(k_1 a) = 0, the transmission coefficient can be made equal to 1. The value of k_1 is determined by the mass of the particle and the difference between the barrier height and the particle's energy.
somebody-nobody
For proton and electron of identical energy encounter same potential barrier .For which probability of transmission greatest?

That depends on the exact height and length of the barrier as well as the energy of the incident particles. For a given height and length of the barrier you can find an energy less than the height of the barrier for which either particle would have a transmission probability of 1 and the other particle would have something less than 1.

You can see a decent treatment of the problem on Wikipedia. Take a look at the form of the transmission coefficient T for the case $E<V_0$. If you choose $k_1$ such that $\sin(k_1 a) = 0$ then the transmission coefficient will be 1. $k_1$ depends on the mass of the particle and the difference between the height of the barrier and the energy of the particle.

The probability of transmission would be greatest for the electron. This is because the electron has a smaller mass compared to the proton, and therefore, it can easily overcome the potential barrier. Additionally, electrons have a wave-like nature, which allows them to exhibit quantum tunneling and pass through barriers that would be impossible for particles with larger mass. Thus, the electron would have a higher chance of transmission compared to the proton in this scenario.

## 1. What is the significance of a proton and electron encountering the same potential?

The encounter of a proton and electron with the same potential is an essential concept in understanding the behavior of charged particles in a given electrical field. It helps in determining the trajectory of particles and can provide insights into the nature of the field itself.

## 2. How does the energy of the proton and electron affect their encounter with the same potential?

The energy of the particles determines the strength of their interaction with the potential. Higher energy particles will experience a greater force and thus may follow a different trajectory compared to lower energy particles.

## 3. Can a proton and electron with different energies still encounter the same potential?

Yes, the energy of the particles is not the determining factor in their encounter with the same potential. As long as their charges and the potential are the same, the particles will have the same interaction regardless of their individual energies.

## 4. How does the mass of the particles affect their encounter with the same potential?

The mass of the particles does not play a significant role in their encounter with the same potential. It may affect their trajectory, but the fundamental interaction with the potential will remain the same.

## 5. Are there any real-world applications of the concept of a proton and electron encountering the same potential?

Yes, this concept is essential in various fields such as electrical engineering, particle physics, and astrophysics. It is used to understand and predict the behavior of charged particles in different environments, such as in particle accelerators or in space.

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