Rutherford's Formula & Alpha Particle Scattering Disagreement

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Homework Help Overview

The discussion revolves around the discrepancies between the Rutherford formula and the scattering of alpha particles at very small angles. Participants are exploring the implications of the formula in the context of nuclear physics and the behavior of alpha particles when interacting with atomic nuclei.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the validity of the problem statement regarding small-angle scattering and its relation to the Rutherford formula. Some suggest that the formula may not account for electron shielding effects, while others express uncertainty about the expected outcomes of small-angle scattering probabilities.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the implications of the Rutherford formula and the role of electrons in scattering processes. There is a notable lack of consensus on whether the problem statement is accurate or if it requires revision based on the physics involved.

Contextual Notes

Some participants mention the need for clarification on whether the small-angle probabilities are predicted to be smaller or larger than those suggested by the Rutherford formula. There are also references to the distances involved in scattering and the forces at play, highlighting potential gaps in the problem's assumptions.

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Homework Statement


Explain why the scattering of \alpha particles at very small angles disagree with the Rutherford formula.

Homework Equations


N/A

The Attempt at a Solution


I find resources from webs and get some information about the failure of Rutherford's formula. It occurs only at the distance of closest approach being less than the diameter of the nucleus and this can happen if (a) the angle of scatter is large or (b) the energy of the particle is large enough, which is on the contrary of the problem statement.

I am thinking the problem statement is wrong.
Could anyone help me?
Regards.
 
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My guess: Very small angles can correspond to very large distances, and then you have electrons to consider, shielding the charge of the nuclei.
 
If you had said "very large scattering angles I would have an answer - at very close distances (~10-14m) the nuclear attraction force subtracts from the Coulomb repulsion force. But I have never heard a problem with the formula for small scattering angles.

Did the statement tell whether the small-angle probabilities are smaller or larger than what the formula predicts?

EDIT: electrons cannot play a part in this because they are so much lighter thsn the alpha particles that they could never get close enough to the alpha particles to cause the latter to veer any appreciable distance (conservation of linear momentum).

EDIT EDIT: I did run across a presentation where the scattering atom's electron cloud can affect the path of the bombarding particle, but this particle had its own electron cloud. I assume alpha particles have no electrons & therefore no electron cloud of their own.
 
Last edited:
rude man said:
If you had said "very large scattering angles I would have an answer - at very close distances (~10-14m) the nuclear attraction force subtracts from the Coulomb repulsion force. But I have never heard a problem with the formula for small scattering angles.

Did the statement tell whether the small-angle probabilities are smaller or larger than what the formula predicts?

EDIT: electrons cannot play a part in this because they are so much lighter thsn the alpha particles that they could never get close enough to the alpha particles to cause the latter to veer any appreciable distance (conservation of linear momentum).

No, the statement here is the only statement I met in the question paper.
This is why I think the statement were wrong.
Thank you!
 
rude man said:
If you had said "very large scattering angles I would have an answer - at very close distances (~10-14m) the nuclear attraction force subtracts from the Coulomb repulsion force. But I have never heard a problem with the formula for small scattering angles.

Did the statement tell whether the small-angle probabilities are smaller or larger than what the formula predicts?

EDIT: electrons cannot play a part in this because they are so much lighter thsn the alpha particles that they could never get close enough to the alpha particles to cause the latter to veer any appreciable distance (conservation of linear momentum).

I'd agree with mfb. The Rutherford formula assumes a bare nucleus. The electrons will screen the central charge at low scattering angles.
 

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