Rutherford Scattering Derivation

In summary, the Rutherford scattering trajectory is derived by considering the conservation of linear momentum and the coulomb force between the incoming particle and the target nucleus. The acceleration is divided into two components - radial and centripetal - which are both dependent on the distance r. The second term, which represents the centripetal acceleration, is an artifact of the polar coordinate system and is independent of the force.
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Dalkiel
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Homework Statement


I'm trying to work out the derivation of the the Rutherford scattering trajectory. I understand the conservation of linear momentum, and that the only force acting is the coulomb force between the incoming particle and the target nucleus. Early on in the derivation I'm told that essentially there are two components to the acceleration, a radial and centripetal. I understand each component separately, but I just don't understand why there are two parts to the acceleration.


Homework Equations


[itex]F = \frac{zZe^{2}}{4\pi\epsilon_{0}r^{2}}=M\left[\frac{d^{2}r}{dt^{2}}-r\left(\frac{d\varphi}{dt}\right)^{2}\right][/itex]

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The Attempt at a Solution


The force is dependent on r, and thus so is the acceleration. The first term on the right (second derivative of position) I understand as the acceleration at a given distance r, and is the radial acceleration. The second term is where I'm running into a bit of trouble. It is the centripetal acceleration, and has a direction opposite that of the radial acceleration. I can also see that it is radial velocity squared times r. I just don't see why it's in the derivation. The acceleration is dependent on r, and we have the first term that takes that into consideration.
 
Physics news on Phys.org

1. What is Rutherford scattering derivation?

Rutherford scattering derivation is a mathematical explanation of how alpha particles, used in the famous Rutherford gold foil experiment, are deflected by the positively charged nucleus of an atom.

2. Why is Rutherford scattering derivation important?

Rutherford scattering derivation helped to disprove the popular "plum pudding" model of the atom and provided evidence for the existence of a small, dense nucleus at the center of an atom.

3. How does Rutherford scattering derivation work?

Rutherford scattering derivation uses Coulomb's law to calculate the repulsive force between the positively charged alpha particles and the positively charged nucleus of the atom. This force causes the particles to be deflected at various angles as they pass through the gold foil.

4. What are the key components of Rutherford scattering derivation?

The key components of Rutherford scattering derivation include the size and charge of the alpha particles, the size and charge of the nucleus, and the thickness and composition of the gold foil used in the experiment.

5. Can Rutherford scattering derivation be applied to other particles?

Yes, Rutherford scattering derivation can be applied to any charged particles, such as protons or electrons, interacting with a positively charged nucleus. It has been used in various experiments to study the structure of different types of atoms.

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