Rutherford’s scattering model assumed one thing only: that alpha particles and nuclei push apart by electrostatic repulsion. And for low and moderate energies, his predictions were spot-on. But when physicists fired alpha particles at higher and higher energies, the results began to peel away from the prediction. Beyond about 27.5 MeV the number of back-scattered alphas dropped far faster than repulsion alone could explain. That gap between prediction and experiment was the first fingerprint of a brand-new force: the strong nuclear force.
📘 What you need to know
Rutherford’s model predicts: as scattering angle increases, the number of alphas scattered decreases
This holds true at low to moderate alpha energies
At very high energies (>~27.5 MeV) the results deviate from Rutherford’s prediction
The number of back-scattered alphas drops sharply to zero instead of the predicted rate
Rutherford assumed only electrostatic repulsion acts between alpha and nucleus
At high energy, alphas get close enough to feel the strong nuclear force (an attraction at very short range)
The strong force acts only over very short distances (<~1.5 fm)
The deviation is therefore evidence for the strong nuclear force
Greatest deviations occur with high-energy alphas and low-nucleon-number target nuclei
What Rutherford predicted
Rutherford’s scattering formula, built entirely on the inverse-square electrostatic repulsion between two positive charges, makes a clear prediction: the higher the alpha energy, the fewer particles bounce straight back, and the count falls off smoothly. Experiments matched this beautifully — up to a point.
Experiment (red) tracks Rutherford’s prediction (blue) until ~27.5 MeV, then plunges sharply to zero. That departure is the clue that repulsion isn’t the whole story.
Why the deviation happens
Rutherford assumed alpha and nucleus interact only through electrostatic repulsion. But if you give the alpha enough energy, it can push past that repulsion and get extremely close to the nucleus — close enough that a different force kicks in.
Below ~27.5 MeV, alphas never get close enough; only electrostatic repulsion acts, and Rutherford’s formula works
Above ~27.5 MeV, alphas get within ~1.5 fm of the nucleus
At that tiny separation, the strong nuclear force takes over — a powerful attraction
This changes the scattering pattern, so the results deviate from Rutherford’s electrostatic-only prediction
Beyond ~3 fm, only the electric repulsion (blue) matters. But squeeze inside ~1.5 fm and the strong nuclear force (red) dominates — a deep attractive well that Rutherford’s model knew nothing about.
Low energy
only repulsion
Rutherford works
high energy, <1.5 fm
Strong force → deviation
The logic that examiners reward: Rutherford’s formula assumes electrostatic force only. So whenever the experiment agrees with it, only electrostatics is acting. When the experiment deviates, something extra must be at play — and that something is the strong nuclear force, which only reaches across ~1.5 fm. The deviation isn’t a failure of the experiment; it’s a discovery.
When are deviations greatest?
To see the biggest deviations, you want the alpha to get as close to the nucleus as possible — into the range where the strong force bites. Two things help.
Condition
Why it increases deviation
High alpha energy
More kinetic energy pushes the alpha closer, into strong-force range
Low nucleon-number target
Less charge means weaker repulsion, so the alpha gets closer at a given energy
WE 1
Alpha particles are fired at a thin gold foil (Z = 79) and the scattering matches Rutherford’s prediction. The gold is then replaced by an aluminium foil (Z = 13) of the same thickness, with alphas of the same energy. Predict how the scattering pattern will differ, and explain why.
Step 1 — compare the nuclear charges
The repulsive force is F = kQq/r², so a smaller nuclear charge means weaker repulsion.
Aluminium (13e) has far less charge than gold (79e).
Step 2 — effect on closest approach
With weaker repulsion, the alpha gets closer to the aluminium nucleus.
Step 3 — the prediction
The alpha can reach the strong-force range at a lower energy for aluminium.
aluminium shows greater deviation from Rutherford scattering than goldThe lower the target’s charge, the closer the alpha penetrates, so the sooner the strong force shows up. That’s why deviations appear most readily with low-Z targets — and why gold, with its huge charge, keeps the alpha at arm’s length and stays “Rutherford-like” longer.
WE 2
The number of back-scattered alpha particles is measured as their energy is increased. (a) Describe what is observed below and above about 27.5 MeV. (b) State what the high-energy behaviour is evidence for.
(a) below and above 27.5 MeV
Below ~27.5 MeV, the count follows Rutherford’s prediction.
Above it, the count drops sharply to zero, deviating from the prediction.
agreement below 27.5 MeV; sharp deviation above it(b) what it’s evidence for
At high energy the alpha reaches within ~1.5 fm and feels an extra attractive force.
evidence for the strong nuclear forceThe magic number ~27.5 MeV is where alphas first get close enough to feel the strong force. Below it, pure electrostatics; above it, the strong force distorts the pattern. Learn that threshold as the marker of “Rutherford breaks down here.”
WE 3
Explain why the deviation from Rutherford scattering provides evidence that the strong nuclear force acts only over a very short range.
Step 1 — when the deviation appears
The deviation only shows up at very high alpha energies.
Step 2 — link energy to distance
Only high-energy alphas get very close (within ~1.5 fm) to the nucleus.
Step 3 — the conclusion
The extra force only appears at these tiny separations, not at larger ones.
the strong force only acts at very short range (~1.5 fm), so it only shows up when alphas get that closeThe chain is: deviation only at high energy → high energy only gets very close → so the new force is short-range. If the strong force reached far out, it would have distorted the low-energy scattering too — but it doesn’t, which pins down its range.
🔬 Answering a deviations question
Rutherford’s assumption: only electrostatic repulsion acts.
Agreement with prediction → only electrostatics; deviation → something extra.
Deviation appears above ~27.5 MeV, when alphas reach ~1.5 fm.
The extra force is the strong nuclear force (attractive, very short range).
Greatest deviation: high alpha energy + low-nucleon-number target.
Short-range evidence: deviation only at high energy = force only acts up close.
💡 Top tips
Rutherford’s formula assumes electrostatic repulsion only — state this first.
Deviation appears above ~27.5 MeV, the threshold to remember.
Deviation = evidence for the strong nuclear force (attractive, range <~1.5 fm).
Greatest deviation with high-energy alphas and low-Z targets.
Deviation only at high energy → the strong force is short-range.
⚠ Common mistakes
Saying the deviation is experimental error — it’s a real physical effect (the strong force)
Forgetting to state Rutherford’s electrostatic-only assumption
Thinking the strong force is repulsive here — at these ranges it’s attractive
Claiming deviations are biggest for high-Z targets — it’s low-Z (alpha gets closer)
Saying the strong force is long-range — it acts only within ~1.5 fm
Ignoring the energy threshold (~27.5 MeV) that marks where Rutherford breaks down
Quick recap: Rutherford’s scattering model assumes only electrostatic repulsion, and it matches experiment at low to moderate alpha energies. But above ~27.5 MeV the number of back-scattered alphas drops sharply, deviating from the prediction, because the alphas get within ~1.5 fm of the nucleus and feel the strong nuclear force — a powerful short-range attraction. This deviation is direct evidence for the strong nuclear force, and it’s greatest for high-energy alphas striking low-nucleon-number nuclei.
We’ve now built the atom from the outside in: a nuclear centre, discrete electron energy levels, and the light those levels produce. The final piece is the model that first explained those energy levels — Niels Bohr’s model of hydrogen, where electrons orbit in fixed shells and their angular momentum is quantised. It even connects to the wave nature of the electron. Next page: Bohr’s Model of Hydrogen.
Deviations and the strong force still fuzzy?
Book a free meeting and we’ll nail the 27.5 MeV threshold, the electrostatic-only assumption, and why deviations reveal the strong force.
