A teaching tape for BM-07, Infer the molecular number
Perrin's count
Open BM-07 with these settings
Where it starts
| Setting | Value |
|---|---|
| Inference temperature (T) | 293.15 |
| Inference viscosity (eta) | 0.001 |
| Inference radius (a) | 5e-7 |
| Displacement count (M) | 50 |
| Observed coordinates (d) | 2 |
| Frame spacing (dt) | 1 |
| Target interval coverage (coverage) | 0.95 |
What it changes, and what to expect
Where it starts, before anything changes
The displacements alone, with the radius not yet declared
Perrin's displacements are already in hand, and on their own they do not pick out a molecular number: they fix only the product of the radius and that number, so any count you like can be had by choosing a radius to match. The instrument says so rather than returning a figure, which is the honest answer to the question as posed and not a failure of the calculation. Open it at these settings to see which outputs it will and will not give you, then read the next step, where declaring the radius is what makes one count identifiable.
Set Independent radius declared (radiusKnown) to true changes how the numbers are read
Declared radius, historical gas-constant set
Before this step the radius is not declared, and the displacements alone fix only the product of radius and molecular number: Avogadro's number comes back underdetermined, which is the honest answer rather than a failure. Declaring the radius independently is what makes the count identifiable, and it is a change of estimator, not of the world: the observations are the same ones. Replay uses the dataset record's own constants. Modern exact k_B is not read.
What the author recorded that a reader should see here. Quantity Expected Under Diffusion coefficient (diffusionCoefficientEstimate) 3.3054 × 10⁻¹³ m²/s scenario-gas-constant-measured radiusNumberProduct 3.91201 × 10¹⁷ m/mol scenario-gas-constant-measured Avogadro number estimate (avogadroNumberEstimate) 7.82402 × 10²³ 1/mol scenario-gas-constant-measured generatorMolecularNumber 7.22789 × 10²³ 1/mol scenario-gas-constant-measured
These are the values the tape's author recorded, not a result this page computed. Nothing here runs the instrument. Open BM-07 with these settings: the link puts them in its form, and it calculates when you apply them. Compare what it gives you with what is recorded here. The settings travel in the link and the laboratory reads them as it loads, so without JavaScript it opens at its worked example instead.
What these numbers were recorded under
| Identity | Recorded as |
|---|---|
| Model | inference-bm07-host version 1 |
| Seed | 1909 |
| Random-stream semantics | version 1 |