# Aplha particle tunneling through coloumb barrier

• kraigandrews
In summary, the conversation discusses approximating the Coulomb barrier of a heavy nucleus using a square potential and using an equation to calculate the probability of an alpha particle with a specific energy tunneling through this barrier. The equation used is T=16(E/V_0)(1-(E/V_0))e^(-2kL). The issue of defining kL>>1 is also mentioned, as it may affect the accuracy of the calculation.
kraigandrews

## Homework Statement

Let us approximate the Coulomb barrier of a heavy nucleus by a square potential with a height of V0 = 14.8 MeV and a width of L = 13.7 fm. What is the probability that an α particle with an energy of 5.70 MeV will tunnel through this barrier?

## Homework Equations

T=16(E/V_0)(1-(E/V_0))e^(-2kL)

## The Attempt at a Solution

essentially it should be a plug and chug however, I cannot get the correct answer. I know the equation above is an approximation given kL>>1 however, what defines that. That could be the only thing I would think that could throw it off.

If someone could explain to me what kL>>1 means and how to apply it to this problem that would be much appreciated. Thanks!

## What is an alpha particle?

An alpha particle is a type of ionizing radiation that consists of two protons and two neutrons bound together. It is commonly emitted by radioactive materials.

## What is a Coulomb barrier?

A Coulomb barrier is an energy barrier that exists between two charged particles, such as an alpha particle and a nucleus. It is caused by the repulsive force between the particles due to their electrical charges.

## How does an alpha particle tunnel through a Coulomb barrier?

An alpha particle can tunnel through a Coulomb barrier by making use of the uncertainty principle in quantum mechanics. This principle allows for the possibility of a particle to exist in a state that it would not be able to classically, leading to a small probability of the particle appearing on the other side of the barrier.

## What factors affect the probability of alpha particle tunneling?

The probability of alpha particle tunneling is affected by several factors, including the energy of the particle, the thickness and height of the barrier, and the mass of the particles involved. Higher energy particles and thinner barriers increase the probability of tunneling, while heavier particles and higher barriers decrease it.

## What are the applications of alpha particle tunneling through Coulomb barriers?

Alpha particle tunneling through Coulomb barriers has various applications in nuclear physics, such as in nuclear fusion reactions and radioactive decay. It is also used in scanning tunneling microscopy, a technique for imaging surfaces at the atomic level.

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