The structure of the atom

Section: Particle Physics  |  Syllabus: Cambridge AS Level Physics (9702)

Early Models of the Atom

For thousands of years, atoms were thought to be indivisible - the smallest particles of matter. However, the discovery of cathode rays in the 1860s challenged this view. Experiments showed these rays were beams of fast-moving, negatively charged particles with mass much smaller than a hydrogen atom - now called electrons.

Since atoms are electrically neutral but contain negative electrons, physicists inferred there must be a positive component. J.J. Thomson proposed the "plum pudding" model: negative electrons were spread evenly through a diffuse (spread out) positive charge, like fruit in a plum pudding.

FIG 11.1: Thomson's Plum Pudding Model

A spherical atom with diffuse positive charge (shaded sphere) containing small negative electrons (minus signs) distributed throughout, like chocolate chips in a muffin. The diffuse positive charge and embedded electrons should be clearly labelled.

The Alpha-Particle Scattering Experiment

In 1908, Ernest Rutherford at the University of Manchester proposed using alpha particles (α-particles) to probe inside the atom. Alpha particles were ideal because they are:

Experimental Setup

The experiment, carried out by Hans Geiger and Ernest Marsden, used the following apparatus:

FIG 11.2: Rutherford's Alpha-Particle Scattering Apparatus

Labelled diagram showing: radium source emitting alpha particles; lead shield confining radiation into a narrow beam; thin gold foil (about 2000 atoms thick) in the centre; circular fluorescent screen surrounding the foil. Arrows indicate particle paths - most going straight through, some deflecting at small angles, and very few bouncing back.

Observations

Observation Proportion
Most α-particles passed straight through undeflected Vast majority
Some α-particles were deflected through small angles Small fraction
Very few α-particles were deflected through angles greater than 90° (back-scattered) About 1 in 20,000
Rutherford's Reaction

Rutherford described the back-scattering result: "It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

Conclusions

The results could not be explained by Thomson's plum pudding model - a diffuse spread of charge could not deflect an α-particle backwards.

Observation Conclusion
Most α-particles passed through undeflected The atom is mostly empty space
Some α-particles deflected through small angles There is a concentration of positive charge in the atom that repels the positive α-particles
Very few α-particles scattered through large angles (>90°) The positive charge and most of the mass is concentrated in a very small region - the nucleus
FIG 11.3: Alpha Particle Paths Through Gold Foil

Cross-section view showing gold atoms as large circles with tiny positive nuclei at their centres. Multiple alpha particle paths shown: (1) most passing straight through empty space, (2) some deflecting at small angles near a nucleus, (3) very few bouncing back at large angles on head-on approach. Label the nucleus, electron cloud, and deflection paths. Note: Diagram not to scale.

Exam Tip

When explaining the scattering experiment, always link each observation to its conclusion. Simply stating the observations without the inferences will not gain full marks.

The Nuclear Model of the Atom

Rutherford proposed a model with a small, dense, positively charged nucleus surrounded by a 'cloud' of electrons. The discovery of the neutron by James Chadwick in 1932 completed the model.

Key features of the nuclear model:

FIG 11.4: Nuclear Model of the Atom

Central nucleus (dense cluster of protons marked + and neutrons) surrounded by orbiting electrons (marked −) at a much larger radius. Include a key: proton (positive), neutron (neutral), electron (negative). Note: Diagram not to scale - the atom is about 10,000 times larger than the nucleus.

Nucleon A particle found in the nucleus; either a proton or a neutron.

Scale of the Nucleus

Rutherford used the experimental results to calculate:

Scale Analogy

If an atom were the size of a sports stadium, the nucleus would be the size of a small marble placed at the centre of the field. All the rest is empty space.

Estimating Nuclear Size: Distance of Closest Approach

The size of the nucleus can be estimated by considering the distance of closest approach of an α-particle fired directly at a nucleus.

FIG 11.5: Distance of Closest Approach

An alpha particle (+2e) approaches a gold nucleus (+79e) along a straight line. The alpha particle slows due to electrostatic repulsion, stops momentarily at distance d from the nucleus, then reverses. Distance d is marked as the "distance of closest approach". Shows kinetic energy converting to electric potential energy.

Derivation

As the positively charged α-particle approaches the positive nucleus, it experiences a repulsive electrostatic force. This force does negative work on the particle, converting its kinetic energy into electric potential energy.

At the point of closest approach (distance d), the α-particle momentarily comes to rest. At this point:

By conservation of energy:

E_k = E_p E_k = (Qq/4π_0 d)

For an α-particle (Q = 2e) approaching a gold nucleus (q = 79e):

E_k = ((2e)(79e)/4π_0 d) = (158e^2/4π_0 d)

Rearranging for d:

d = (158e^2/4π_0 E_k) Worked Example: Estimating Nuclear Diameter

An α-particle with initial kinetic energy 8 × 10^-13 J is fired at a gold nucleus (charge +79e). Calculate the distance of closest approach.

Solution

Using: d = (Qq/4π_0 E_k)

d = (2 × 1.60 × 10^-19)(79 × 1.60 × 10^-19)4π(8.85 × 10^-12)(8 × 10^-13)

d ≈ 4.5 × 10^-14 m

This gives an upper estimate for the nuclear diameter (the actual nucleus must be smaller than this for the α-particle to have turned around without touching it).

Interactive revision notes, videos and practice questions load below.

Related: Past Papers Topical Questions IGCSE Physics A2 Physics Grade Boundaries Command Words