Structure of the Atom
3. High-Energy Scattering Experiments
Learning Outcomes
- I can describe how scattering experiments provide information about atomic structure.
- I can explain the results of Rutherford's gold foil experiment.
- I can describe how high-energy electrons are used to probe nuclei.
- I can explain how scattering angles reveal structural information.
- I can evaluate evidence obtained from scattering experiments.
How Can We Study Something Too Small to See?
Atoms and atomic nuclei are far too small to examine directly with an ordinary microscope. Instead, scientists can investigate their structure by firing particles at them and studying what happens.
This technique is called scattering.
The basic idea is simple:
- Fire particles toward a target.
- Detect where the particles go after interacting with the target.
- Measure how much their paths change.
- Use the pattern of scattering to infer the structure of the target.
This is similar to trying to determine the shape of an invisible object by throwing small balls toward it and observing how the balls bounce away.
Scattering experiments have provided some of the most important evidence for our modern understanding of atomic and nuclear structure.
Rutherford's Gold Foil Experiment
One of the most famous scattering experiments was carried out in the early twentieth century by Hans Geiger and Ernest Marsden, working under the direction of Ernest Rutherford.
The experiment tested the accepted model of the atom at the time.
According to the plum pudding model, the atom consisted of positive charge spread throughout the atom, with negatively charged electrons embedded within it.
If this model were correct, a fast-moving positively charged particle passing through an atom should experience only relatively small deflections.
The scattering experiment showed something very different.
The Experimental Setup
The experiment used alpha particles.
Alpha particles are:
- Positively charged
- Relatively massive compared with electrons
- Fast-moving when emitted by radioactive materials
A radioactive source produced a narrow beam of alpha particles.
The beam was directed toward a very thin sheet of gold foil.
A detector surrounding the foil allowed the researchers to determine where the alpha particles travelled after passing through or interacting with the gold atoms.
Gold was useful because it can be made into extremely thin sheets only a few hundred atoms thick.
What Scientists Expected
Under the plum pudding model, the positive charge of an atom was thought to be spread throughout its volume.
Because this positive charge was diffuse, scientists expected the alpha particles to pass through the foil with only small changes in direction.
The expected result was therefore:
Almost all alpha particles should travel approximately straight through the foil.
Large-angle deflections were not expected.
Particles travelling backward toward the source seemed especially unlikely.
What They Actually Observed
The experiment produced three important observations.
Most Alpha Particles Passed Straight Through
The overwhelming majority of alpha particles passed through the gold foil with little or no change in direction.
Some Alpha Particles Were Deflected
A smaller number changed direction as they passed through the foil.
Some experienced noticeable deflections.
A Very Small Number Were Deflected Through Large Angles
A tiny fraction of the alpha particles were scattered through very large angles.
Some even travelled approximately back toward the source.
This final observation was especially surprising.
What Did the Results Mean?
Scientists needed a model of the atom that could explain all three observations.
Most Particles Passed Straight Through
This suggested that most of an atom's volume contains relatively little matter capable of strongly deflecting an alpha particle.
Therefore:
Most of the atom is empty space.
Some Particles Were Deflected
Because alpha particles are positively charged, their deflection suggested that they were being repelled by another concentration of positive charge.
Therefore:
The positive charge of the atom must be concentrated rather than spread uniformly throughout the atom.
A Few Particles Were Strongly Deflected
Large-angle scattering required a very strong interaction concentrated within a very small region.
This suggested that most of the atom's mass and positive charge were concentrated in a tiny central region.
This region became known as the nucleus.
The Nuclear Model of the Atom
The evidence led to a new model of atomic structure.
According to the nuclear model:
- The atom contains a very small central nucleus.
- The nucleus contains positive charge.
- Most of the atom's mass is concentrated in the nucleus.
- The nucleus occupies only a tiny fraction of the atom's total volume.
- Most of the atom is empty space.
- Electrons occupy the region surrounding the nucleus.
This model replaced the plum pudding model.
Evidence and Conclusions
A useful way to understand Rutherford scattering is to connect each observation directly to a conclusion.
| Observation | Evidence about atomic structure |
|---|---|
| Most alpha particles passed straight through | Most of the atom is empty space |
| Some particles were deflected | Positive charge is concentrated within the atom |
| Very few particles were strongly deflected | The concentrated positive region is extremely small |
| Some particles scattered backward | The nucleus is dense and capable of producing very strong repulsive interactions |
The strength of the experiment was not simply that particles scattered. It was the pattern and frequency of different scattering angles that provided information about the atom.
Why Positive Alpha Particles Are Deflected
Alpha particles have a positive electric charge.
The atomic nucleus also has a positive charge.
Like charges repel.
An alpha particle passing far from a nucleus experiences relatively little repulsion and therefore changes direction only slightly.
An alpha particle passing closer to the nucleus experiences a much stronger repulsive force and is deflected through a larger angle.
A particle approaching the nucleus very closely can experience a very large deflection.
Scattering Angle
The scattering angle describes how much the direction of a particle changes during an interaction.
A small scattering angle means the particle's path changed only slightly.
A large scattering angle means the particle experienced a much greater change in direction.
The distribution of scattering angles provides information about the structure of the target.
In Rutherford scattering:
Small deflection → particle passed relatively far from a nucleus
Large deflection → particle passed relatively close to a nucleus
Very large or backward deflection → particle experienced a particularly strong interaction with a nucleus
The exact relationship is more complicated than this simple description, but the central principle remains: the pattern of scattering reveals information about structures that cannot be directly seen.
Why Large-Angle Scattering Was So Important
The rare large-angle deflections were particularly significant.
A model with positive charge spread throughout the atom could not easily explain how a heavy, fast-moving alpha particle could suddenly change direction by a large amount.
A small, concentrated positive nucleus could.
The rarity of these events was also important.
If the nucleus occupied a large fraction of the atom, large deflections would have occurred much more frequently.
Instead, they were rare.
This provided evidence that the nucleus occupies a very small fraction of the atom's volume.
From Alpha Particles to High-Energy Electrons
The same basic idea can be taken much further.
Modern scattering experiments can use high-energy electrons as probes.
Electrons are accelerated to very high speeds and directed toward a target.
Detectors then measure:
- How many electrons pass through
- How many are scattered
- Their scattering angles
- Their energies after scattering
Scientists compare the observed scattering pattern with predictions from different models of nuclear structure.
Why Use High-Energy Electrons?
Electrons are useful probes because they are extremely small and interact electrically with charged particles in the nucleus.
Increasing the energy of the electrons also improves their ability to investigate very small structures.
In general:
Higher-energy particles can probe smaller distance scales.
This is related to the wave behaviour of matter.
Particles such as electrons have an associated wavelength. As their momentum increases, their wavelength becomes shorter.
Shorter wavelengths allow scientists to investigate smaller structures, much as shorter-wavelength electromagnetic radiation can reveal finer details than longer-wavelength radiation.
Electron Wavelength and Resolution
The wavelength associated with a particle is described by the de Broglie relationship:
λ = h / p
where:
- λ = wavelength
- h = Planck's constant
- p = momentum
You do not always need to calculate this relationship to understand scattering experiments.
The important idea is:
Greater momentum → shorter wavelength → ability to probe smaller structures
This is one reason particle accelerators are designed to produce extremely high-energy beams.
How Electron Scattering Reveals Nuclear Structure
Imagine firing high-energy electrons toward a nucleus.
If the nucleus behaved exactly like a tiny point charge, scientists would expect a particular scattering pattern.
If the experimental results differ from that prediction, the difference provides evidence that the nucleus has internal size and structure.
By carefully analysing:
- scattering angles
- numbers of scattered particles
- particle energies
- scattering probabilities
scientists can estimate properties such as:
- nuclear size
- charge distribution
- internal nuclear structure
Scattering therefore acts as an indirect form of imaging.
A Useful Analogy: Exploring an Invisible Object
Imagine that you are standing in a dark room containing an invisible object.
You throw hundreds of small balls toward it.
Suppose:
- Most continue straight.
- Some bounce slightly sideways.
- A few bounce sharply backward.
Even though you cannot see the object, the paths of the balls give you information about:
- Its location
- Its size
- Its shape
- How solid or concentrated it is
Particle scattering uses the same basic reasoning, but at atomic and subatomic scales.
Scattering Patterns
Scientists do not usually draw conclusions from a single scattered particle.
Instead, they examine large numbers of scattering events.
The result is a scattering pattern or distribution.
For example, scientists might measure how many particles are detected at:
- 10°
- 20°
- 30°
- 60°
- 90°
- 120°
- 150°
A successful scientific model should predict a scattering distribution that agrees with the experimental observations.
Models Make Predictions
Scattering experiments are powerful because scientific models make testable predictions.
The general process is:
Model → prediction → experiment → evidence → evaluation
For example, the plum pudding model predicted that large-angle alpha-particle scattering should be extremely unlikely.
The experimental observations showed significant deviations from what that model could explain.
Scientists therefore needed to revise the model.
The nuclear model provided a much better explanation of the evidence.
This is an important example of how scientific knowledge develops.
Evaluating Evidence from Scattering Experiments
Good scientific evidence should be evaluated carefully.
Scientists consider questions such as:
- Were enough particles detected?
- Were the measurements repeatable?
- How accurately were scattering angles measured?
- Could background radiation affect the results?
- Could the particles interact with something other than the intended target?
- Does the proposed model explain the entire scattering pattern?
- Do independent experiments produce similar results?
A model becomes more convincing when it successfully explains many observations and makes predictions that are confirmed by further experiments.
Evidence Does Not Give a Direct Photograph
A scattering experiment does not normally produce a direct photograph of a nucleus.
Instead, scientists make inferences from measurements.
For example:
Observation: Very few alpha particles scatter backward.
Inference: A very small region of the atom can produce extremely strong repulsion.
Model: The atom contains a tiny, dense, positively charged nucleus.
It is important to distinguish between the observation and the interpretation of that observation.
Scattering and Scientific Models
Scientific models are not simply guesses.
A useful model must:
- Explain existing observations
- Agree with experimental evidence
- Make testable predictions
- Be modified or rejected if new evidence contradicts it
Rutherford's work is a classic example.
The gold foil results did not fit the existing atomic model, so scientists developed a model that better explained the evidence.
Later experiments refined the nuclear model even further.
From the Atom to the Nucleus
Rutherford scattering showed that atoms contain nuclei.
Later, higher-energy scattering experiments allowed scientists to investigate the nuclei themselves.
As experimental energies increased, scientists were able to probe increasingly small scales.
This eventually contributed to evidence that protons and neutrons are themselves not fundamental particles but have an internal structure involving quarks.
Why Higher Energy Reveals Smaller Structures
This is one of the most important ideas in modern experimental physics.
To investigate something extremely small, scientists need a probe capable of resolving structures at that scale.
Higher-energy particles generally have shorter associated wavelengths.
Therefore:
Low energy → longer wavelength → less detail
High energy → shorter wavelength → greater ability to investigate small structures
Modern particle accelerators use this principle to investigate matter at scales far smaller than atomic nuclei.
Comparing Rutherford and Modern Scattering Experiments
| Feature | Rutherford scattering | Modern high-energy scattering |
|---|---|---|
| Probe | Alpha particles | Often electrons or other high-energy particles |
| Target | Thin gold foil | Nuclei, protons, or other particles |
| Measurement | Scattering direction | Angle, energy, momentum and other properties |
| Main purpose | Investigate atomic structure | Investigate nuclear and subnuclear structure |
| Key idea | Scattering reveals hidden structure | Scattering reveals hidden structure |
Although the technology has changed enormously, the underlying reasoning is remarkably similar.
Common Mistakes
Saying All Alpha Particles Were Deflected
Most alpha particles passed through the gold foil with little or no deflection.
Only a small fraction were significantly deflected.
Saying Rutherford Discovered That Atoms Are Solid
The experiment provided evidence for almost the opposite conclusion.
Most of the atom is empty space.
Saying the Nucleus Is Large
The nucleus contains most of the atom's mass but occupies only a tiny fraction of its volume.
Dense does not mean large.
Confusing Electrons with Alpha Particles
Rutherford's gold foil experiment used alpha particles, not electrons.
High-energy electron scattering refers to later experiments used to probe smaller structures.
Assuming Large Scattering Angles Are the Most Common
Large-angle scattering is relatively rare.
Its rarity is itself important evidence about the small size of the nucleus.
Treating the Atomic Model as a Direct Observation
Scientists do not directly see the nucleus in Rutherford scattering.
They infer its existence and properties from the scattering evidence.
Ignoring the Importance of Scattering Angle
The amount of deflection provides information about the strength and nature of the interaction.
Scattering angle is therefore a key experimental measurement.
Check Your Understanding
1. What is a scattering experiment?
2. Why are scattering experiments useful for studying atoms and nuclei?
3. What type of particle was used in Rutherford's gold foil experiment?
4. What happened to most of the alpha particles?
5. What happened to a small number of alpha particles?
6. What was particularly surprising about a very small fraction of the particles?
7. What did the large number of particles passing straight through suggest about atomic structure?
8. What did large-angle scattering suggest about the distribution of positive charge?
9. Explain why large-angle scattering events were relatively rare.
10. Why are alpha particles repelled by an atomic nucleus?
11. What information can scientists obtain from scattering angles?
12. Why are high-energy electrons useful for investigating nuclei?
13. Explain why higher-energy particles can investigate smaller structures.
14. Why do scientists examine large numbers of scattering events rather than relying on one particle?
15. Explain how Rutherford's experiment demonstrates the relationship between experimental evidence and scientific models.
Key Terms
- Scattering – the change in direction of a particle caused by an interaction with another particle or structure.
- Scattering experiment – an experiment in which particles are directed toward a target and their resulting paths are measured.
- Alpha particle – a positively charged particle consisting of two protons and two neutrons.
- Gold foil experiment – the experiment in which alpha-particle scattering provided evidence for the nuclear atom.
- Scattering angle – the angle through which a particle's direction changes during an interaction.
- Nucleus – the tiny, dense, positively charged central region of an atom.
- Nuclear model – a model of the atom in which most mass and positive charge are concentrated in a small nucleus.
- High-energy electron – an electron accelerated to high energy for use as a probe of small structures.
- de Broglie wavelength – the wavelength associated with a moving particle.
- Resolution – the ability to distinguish small or closely spaced structures.
- Inference – a conclusion reached from observations and evidence.
- Scattering pattern – the distribution of particles detected after a scattering experiment.
Key Takeaways
- Scattering experiments allow scientists to investigate structures that are too small to observe directly.
- Rutherford's experiment fired alpha particles at thin gold foil.
- Most alpha particles passed straight through, showing that most of an atom is empty space.
- Some alpha particles were deflected, showing that positive charge is concentrated within the atom.
- Rare large-angle deflections provided evidence for a tiny, dense, positively charged nucleus.
- Scattering angle provides information about the interaction between a probe particle and the target.
- High-energy electrons can be used to investigate nuclear structure.
- Higher-energy particles have shorter associated wavelengths and can probe smaller distance scales.
- Scientists analyse large numbers of scattering events to identify reliable patterns.
- Scattering experiments provide indirect evidence: scientists infer structure from measured particle behaviour.
- Scientific models can be tested by comparing their predicted scattering patterns with experimental results.
- When experimental evidence disagrees with a model, the model may need to be modified or replaced.