# Alpha Particle shot at Nucleus Energy

• pearbear21
In summary, the question is asking for the energy of an alpha particle needed to just reach the surface of an Al nucleus with a radius of 4fm. The equation used for this calculation is the Coulombic force equation. The attempted solution involved integrating this equation from infinity to 4X10^-15m, but the resulting value seemed unreasonable. The correct method is to use conservation of energy and calculate the final electrostatic energy of the system at the point of closest approach. This can be done by finding the distance of closest approach using the equation rd = kqQ/.5mv^2.
pearbear21

## Homework Statement

What energy alpha particle would be needed to just reach the surface of an Al nucleus if its radius is 4fm?

*This problem is found in a section dealing with Rutherford's gold foil scattering experiment, so take it in that context.

F=(kqQ)/r2

## The Attempt at a Solution

I assume the book (Modern Physics by Tipler and Llewellyn ed. 5) wants this performed a classical manner, so I started by considering the energy of the particle as an integral of the coulombic force equation from r=$$\infty$$ to r=4X10-15m.

so, kqQ$$\int$$r-2dr=kqQ[-r-1]

evaluated from $$\infty$$ to 4X10-15m gives a value of -1.4995992X10-12 Joules. This seems quite unreasonable as the repulsion seems intuitively large at such small distances and a joule is a small unit to begin with.

What do you think of my method and answer? Do you feel there is a different way I should have approached the problem? At first, I tried finding the force to hold the alpha particle just on the surface of the Al nucleus, but after finding that force couldn't find a way to convert to energy correctly.

The energy you are trying to calculate is the final electrostatic energy of the system. When the alpha particle is fired with zero impact parameter, the initial kinetic energy of the alpha particle is entirely converted into electrostatic energy at the point of closest approach. Just use conservation of energy.

Thanks, I think I figured it out upon further inspection of the text. rd, distance of closest approach, may be calculated as follows:

rd = kqQ/.5mv2

## What is an alpha particle?

An alpha particle is a positively charged particle that consists of two protons and two neutrons. It is the most common type of radiation emitted by radioactive materials.

## What happens when an alpha particle is shot at a nucleus?

When an alpha particle is shot at a nucleus, there is a high chance that it will be repelled due to the strong electrostatic forces between the positively charged alpha particle and the positively charged nucleus. However, in some cases, the alpha particle may be absorbed by the nucleus, causing it to become unstable and possibly undergo radioactive decay.

## What is the energy of an alpha particle?

The energy of an alpha particle can vary, but typically ranges from 4 to 8 MeV (million electron volts). This energy is relatively low compared to other types of radiation, such as beta particles or gamma rays.

## How does the energy of an alpha particle affect its ability to penetrate matter?

Due to its relatively low energy, an alpha particle can only travel a short distance in air (a few centimeters) and can be stopped by a sheet of paper or even the outer layers of human skin. However, if an alpha particle is emitted inside the body (for example, in the case of internal exposure to a radioactive source), it can cause significant damage to tissues and organs due to its high ionizing ability.

## What are the potential applications of shooting alpha particles at nuclei?

Shooting alpha particles at nuclei can be used in nuclear physics research to study the structure and properties of atomic nuclei. It can also be used in medical applications, such as in radiation therapy for cancer treatment. Additionally, alpha particles are used in smoke detectors to detect the presence of smoke particles in the air.

Replies
29
Views
7K
Replies
3
Views
1K
Replies
2
Views
13K
Replies
5
Views
1K
Replies
3
Views
7K
Replies
4
Views
6K
Replies
1
Views
5K
Replies
6
Views
2K
Replies
9
Views
5K
Replies
1
Views
1K