Comparing historical changes in physical models

The historical development of atomic models is a sequence of refinements driven by new experimental data. Thomson's "plum pudding" model described the atom as a cloud of positive charge with embedded electrons, but Rutherford's $\alpha$-particle scattering experiment showed that nearly all the mass and positive charge are concentrated in a small nucleus. Rutherford's nuclear model explained the scattering, yet it contradicted the observed line spectra: classical electrodynamics predicted continuous radiation and a rapid collapse of the electron into the nucleus. Bohr introduced postulates of stationary orbits and quantized radiation $hf = E_m - E_n$, which allowed the hydrogen spectrum to be calculated. The quantum-mechanical model replaced definite orbits with probabilistic orbitals and agrees with finer effects, such as line splitting in a magnetic field. When comparing models, it is important to match their predictions against specific evidence and to identify which observation forced a model to change.

In an experiment a thin gold foil is bombarded with a beam of $\alpha$-particles. It is observed that most particles pass through with almost no deflection, a small fraction is deflected through large angles, and some bounce back. Which atomic model does this result support, and which does it refute? Explain briefly.

In the Bohr model the electron energy in a hydrogen atom is $E_n = -13.6/n^2$ eV. The electron transitions from level $n=3$ to level $n=2$. Calculate the emitted photon energy and wavelength, using $hc = 1240$ eV·nm. Explain why one discrete line in the spectrum supports the Bohr model.

In a strong magnetic field a single hydrogen spectral line predicted by the Bohr model splits into three closely spaced lines. The Bohr model describes the electron on a single orbit and does not include the electron's intrinsic magnetic moment. Evaluate which model better explains this observation and state one criterion that a revised model must satisfy.

A safe self-study activity using a simulation. Open the PhET simulation "Models of the Hydrogen Atom" or an equivalent. 1. In "Experiment" mode, turn on the light source and observe the hydrogen line spectrum. 2. One by one, select the models: billiard ball, plum pudding, classical solar system, Bohr, quantum-mechanical. 3. For each model, record whether the predicted spectrum matches the observed one. 4. Make a table: model — key assumption — agreement with experiment — reason for discrepancy. 5. Write an evidence-based conclusion: which model best matches the spectrum and why. Work at the computer for no more than 30 minutes, taking breaks for your eyes.

The purpose of the visualization is to show how the predictions of each historical atomic model relate to two key sets of evidence: $\alpha$-particle scattering and the hydrogen line spectrum.

A timeline diagram: from left to right are the models (billiard ball, plum pudding, nuclear, Bohr, quantum-mechanical) with simple sketches. Below each model is a mini-graph: for the Rutherford experiment, the angular distribution of scattered particles; for the spectrum, a set of vertical lines, where solid lines show the observed hydrogen spectrum and dashed lines show the model's prediction. A legend explains that a mismatch between the dashed and solid lines indicates that the model must be changed.

You stand outside and count the seconds between the flash and the bang: $3\ \text{s}$. Sound travels at $343\ \text{m/s}$ at $20^\circ\text{C}$, so the strike is $343 \times 3 \approx 1030\ \text{m} \approx 1\ \text{km}$ away. A nearby strike carries a current near $30\ \text{kA}$ at a potential difference of about $10^8\ \text{V}$ for a few tens of microseconds — enough to split a tree trunk.

This is model comparison in action. Aristotle explained thunder as clouds colliding; Franklin's kite experiment (1752) showed lightning is an electric discharge, and today the same event is described by charge separation followed by electron transfer — a model that grew out of the quantum picture of the atom. The checkable numbers — the $3\ \text{s}$ interval and the sound speed $343\ \text{m/s}$ — are what let you test a model and decide which one survives.

Your phone fixes your position to within $5\ \text{m}$. The satellites orbit at $20\,200\ \text{km}$ altitude with speed $3.87\ \text{km/s}$, and each carries an atomic clock referenced to the caesium-133 transition at $9\,192\,631\,770\ \text{Hz}$ — the definition of the second. Relativity predicts the satellite clock gains about $38\ \mu\text{s}$ per day; uncorrected, that time error times the speed of light gives $38 \times 10^{-6} \times 3 \times 10^8 \approx 11\ \text{km}$ of position error per day.

Two historical models meet in this screen. Newtonian mechanics assumes one universal time and predicts the orbit correctly, but it fails for the clock; the special- and general-relativistic corrections replace it. The clock itself rests on the quantum model: the caesium atom jumps between discrete energy levels, exactly the step from the elastic-sphere atom to the quantized-orbit atom. Comparing what each model does and does not predict is the skill this lesson trains.

A microwave labelled $800\ \text{W}$ at $2.45\ \text{GHz}$ heats $250\ \text{g}$ of water from $20^\circ\text{C}$ to $80^\circ\text{C}$. The energy required is $Q = mc\Delta T = 0.25 \times 4186 \times 60 \approx 6.3 \times 10^4\ \text{J}$, so at full power it takes $6.3 \times 10^4 / 800 \approx 79\ \text{s}$. A single microwave photon carries $E = h\nu = 6.63 \times 10^{-34} \times 2.45 \times 10^9 \approx 1.6 \times 10^{-24}\ \text{J}$, that is about $10^{-5}\ \text{eV}$.

That tiny photon energy is the decisive number for comparing models. It is far below the $13.6\ \text{eV}$ needed to ionize a hydrogen atom, so the radiation can only set water molecules rotating and vibrating — it heats, but cannot tear electrons out of atoms. The 18th-century caloric fluid, the 19th-century kinetic theory of heat and the quantum model of discrete rotational levels each account for part of the same $79\ \text{s}$, and this lesson asks which measurement killed which model.