Rutherford's Formula & Alpha Particle Scattering Disagreement

• rbwang1225
In summary: For the very high scattering angles, you need to assume that the alpha particle collides with a single nucleus. At smaller angles, the alpha particle may also interact with the electron cloud of the target atom.In summary, the scattering of alpha particles at very small angles does not agree with the Rutherford formula due to the presence of electrons and the resulting screening of the central charge at low angles. In addition, at very small distances, the alpha particle may also interact with the electron cloud of the target atom, further affecting the scattering results.
rbwang1225

Homework Statement

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

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.

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.

1. What is Rutherford's formula?

Rutherford's formula, also known as the Rutherford scattering formula, is a mathematical equation that describes the scattering of alpha particles by a nucleus. It is based on the principles of classical mechanics and was proposed by physicist Ernest Rutherford in 1911.

2. How does the Rutherford formula explain alpha particle scattering?

The Rutherford formula states that the probability of an alpha particle being scattered at a certain angle is inversely proportional to the fourth power of the sine of half the angle of scattering. This means that the majority of alpha particles will be scattered at small angles, while only a few will be scattered at large angles.

3. What was the disagreement with alpha particle scattering that Rutherford's formula addressed?

When Rutherford first conducted his famous gold foil experiment, he observed that most of the alpha particles passed straight through the foil, while a small percentage were scattered at large angles. This was unexpected, as the prevailing model at the time predicted that the positive charge of the nucleus would cause all alpha particles to be deflected at small angles.

4. How did Rutherford's formula resolve the disagreement with alpha particle scattering?

Rutherford's formula showed that the scattering of alpha particles was not random, but rather followed a predictable pattern. It accurately described the distribution of alpha particle scattering angles observed in the experiment, providing evidence for the existence of a small, positively charged nucleus within the atom.

5. Is Rutherford's formula still used today?

While the Rutherford formula is still used as a basic model for understanding alpha particle scattering, it is not considered a complete description of the process. It does not take into account the quantum nature of particles, and has been superseded by more advanced models such as the quantum mechanical scattering theory.

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