# Energy needed to tunnel through a potential barrier

• Tester_Boy
In summary, tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier despite not having enough energy to overcome it. The energy needed for tunneling is calculated using the Schrödinger equation and can be affected by the height, width, and shape of the barrier as well as the mass of the particle. It can be manipulated by changing the properties of the barrier and has practical applications in the development of tunneling microscopes, electronic devices, and nuclear fusion.
Tester_Boy

## Homework Statement

An electron approaches a potential barrier 10 eV high and 0.5 nm wide. If the electron has a
1% chance of tunnelling through, what must be its energy?

## Homework Equations

don't know how to put equations in eg how do i get something like alpha and theta etc

## The Attempt at a Solution

ended up with a massive equations with E's all over the place and imposible to solve :(

Show how you tried to solve this problem. What is the transmission coefficient expression you are using?

## 1. What is the concept of "tunneling" in regards to potential barriers?

Tunneling refers to the phenomenon in quantum mechanics where a particle can pass through a potential barrier despite not having enough energy to overcome it. This occurs due to the wave-like nature of particles, which allows them to exist in multiple states simultaneously and thus have a non-zero probability of appearing on the other side of the barrier.

## 2. How is the energy needed to tunnel through a potential barrier calculated?

The energy needed to tunnel through a potential barrier is calculated using the Schrödinger equation, which describes the wave function of a particle in quantum mechanics. The wave function is used to determine the probability of a particle being in a particular state, including the state on the other side of the barrier.

## 3. What factors affect the amount of energy needed for tunneling?

The main factors that affect the energy needed for tunneling are the height and width of the potential barrier. A higher and wider barrier requires more energy for a particle to tunnel through. Additionally, the mass of the particle and the shape of the barrier also play a role in the energy needed for tunneling.

## 4. Can the energy needed for tunneling be manipulated?

Yes, the energy needed for tunneling can be manipulated by changing the properties of the potential barrier. For example, by decreasing the height or width of the barrier, the energy needed for tunneling decreases. Additionally, by changing the shape of the barrier, the energy needed for tunneling can also be altered.

## 5. What practical applications does the concept of tunneling have?

Tunneling has many practical applications, such as in the development of tunneling microscopes, which use the phenomenon to produce highly detailed images of objects on a nanoscale. Tunneling also plays a crucial role in the functioning of electronic devices, such as tunnel diodes and flash memory, and in the process of nuclear fusion in stars.

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