Rutherford's Formula & Alpha Particle Scattering Disagreement

[rbwang1225]

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.

 

[mfb]

My guess: Very small angles can correspond to very large distances, and then you have electrons to consider, shielding the charge of the nuclei.

 

[rude man]

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.

 

[rbwang1225]

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!

 

[Dick]

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.