# What is the probability of an alpha particle escaping from a nucleus?

• crimson.red
In summary, the conversation discusses a simple model of alpha decay and the probability of an alpha particle escaping from a nucleus. The dimensions of the barrier and the average barrier height are provided, along with the transmission probability equation. The question asks for the probability of an alpha particle escaping in a day. The attempt at a solution involves using a formula but results in a strange answer.
crimson.red

## Homework Statement

We consider a simple model of alpha decay. Imagine an alpha particle moving around inside a nucleus. When the alpha bounces against the surface of the nucleus, it meets a barrier caused by the attractive nuclear force. The dimensions of this barrier vary a lot from one nucleus to another, but as representative numbers you can assume that the barriers width is 35 fm and the average barrier height U0 x E = 5MeV. Find the probability that an alpha particle hitting the nuclear surface will escape. Given that the alpha hits the nuclear surface about 5x10^21 times per sec, what is the probability that it will escape in a day?

## Homework Equations

Transmission probability is given by:
T(E) = {1+1/4[U^2/E(U-E)]sinh^2ALPHA*L}^-1
ALPHA = sqrt(2m(U-E))/h.bar

There are 86400s in a day: 4.32E36 alpha-hit

## The Attempt at a Solution

I tried using E = (h.bar^2 x k^2)/2m but then it gives me a really really weird answer. Can anyone help me crack this problem?

My E

The E that I got using the above formula is 2.633E15!

## 1. What is the tunneling effect?

The tunneling effect is a quantum phenomenon where a particle can pass through a potential barrier that it does not have sufficient energy to overcome.

## 2. How does the tunneling effect occur?

The tunneling effect occurs due to the wave-like nature of particles at the quantum level. The particle has a probability of existing on the other side of the potential barrier, allowing it to tunnel through.

## 3. What is the significance of the tunneling effect in science?

The tunneling effect is significant in various fields of science, including quantum mechanics, nuclear physics, and solid-state physics. It plays a crucial role in explaining the stability of atomic nuclei, the functioning of tunnel diodes, and the tunneling microscopy technique.

## 4. What are some real-world applications of the tunneling effect?

The tunneling effect has several practical applications in technology, such as in scanning tunneling microscopes, which are used to study surfaces at the atomic level. It is also utilized in tunnel diodes, which are important components in electronic devices like computers and cell phones.

## 5. Can the tunneling effect be observed in everyday life?

The tunneling effect is not easily observable in everyday life as it occurs at the quantum level. However, it has been observed in certain natural phenomena, such as radioactive decay and nuclear fusion processes in stars.

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