SCIENCE · INVESTIGATE AND EXPLAIN

Separate a spectral threshold from an instrument intercept

A stopping-potential line is a measurement model, not an automatic work-function measurement. For above-threshold photons, Einstein energy balance gives eVs=hf−phi. Here frequency f is reported in units of 10^14 Hz and the supplied rounded slope is 0.4135667696 V per frequency unit. The instrument adds an unknown voltage offset B but has independently assumed unit gain. Its indication is y=m f−phi/e+B.

Learning outcome: Fit the two unknown-material records without using the generating work function or offset. Freeze the third prediction. Then add the independent reference material and recover the threshold. Change only the offset and identify which fitted quantities remain unchanged. Retain a gain-error alternative.

Starting recap

Review definite integrals, complex amplitudes, probability moments, elementary differential equations and energy-momentum units. State boundary and normalization conditions, and distinguish calibration from unused validation.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

For work function 2 eV and offset 0.1 V, the first two indications are 1.4085341568 and 2.235667696 V. Their slope is 0.4135667696 and intercept −1.9 V, predicting 3.0628012352 V at frequency 12. The reference-material indication at 10 is 1.235667696 V; it identifies offset 0.1 V and hence work function 2 eV.

Open the experiment

Predict

Without the reference material, which combination is identified by the fitted intercept?

Your prediction and reason

Experiment

Fit the two unknown-material records without using the generating work function or offset. Freeze the third prediction. Then add the independent reference material and recover the threshold. Change only the offset and identify which fitted quantities remain unchanged. Retain a gain-error alternative.

Identify a threshold only with an independent reference

Worked teaching model · synthetic values · Above-threshold synthetic stopping indications y=hfreq f−phi+B, f in 10^14 Hz and hfreq=.4135667696 V per frequency unit. Unknown material records at f8,10 calibrate slope/intercept; f12 is fresh. A separate independently known reference work function3 eV at f10 uses the same additive offset and unit gain. Without that reference, phi and offset cannot be separated. No physical UV or electrode activity.

Generating unknown-surface work function: 2 eV Shared additive stopping-readout offset: 0.1 V

Reset keeps your prediction, captures and practice history.

Above-threshold calibration and unused frequency

Graph axes rescale independently; read units and values, not screen angles. 1: first-two-record linear fit (solid).2: fresh frequency record (open-circle marked location). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Above-threshold calibration and unused frequency

first-two-record linear fit

frequency (10^14 Hz)	stopping indication (V)
8	1.408534
8.066667	1.436105
8.133333	1.463676
8.2	1.491248
8.266667	1.518819
8.333333	1.54639
8.4	1.573961
8.466667	1.601532
8.533333	1.629103
8.6	1.656674
8.666667	1.684245
8.733333	1.711816
8.8	1.739388
8.866667	1.766959
8.933333	1.79453
9	1.822101
9.066667	1.849672
9.133333	1.877243
9.2	1.904814
9.266667	1.932385
9.333333	1.959957
9.4	1.987528
9.466667	2.015099
9.533333	2.04267
9.6	2.070241
9.666667	2.097812
9.733333	2.125383
9.8	2.152954
9.866667	2.180525
9.933333	2.208097
10	2.235668
10.06667	2.263239
10.13333	2.29081
10.2	2.318381
10.26667	2.345952
10.33333	2.373523
10.4	2.401094
10.46667	2.428666
10.53333	2.456237
10.6	2.483808
10.66667	2.511379
10.73333	2.53895
10.8	2.566521
10.86667	2.594092
10.93333	2.621663
11	2.649234
11.06667	2.676806
11.13333	2.704377
11.2	2.731948
11.26667	2.759519
11.33333	2.78709
11.4	2.814661
11.46667	2.842232
11.53333	2.869803
11.6	2.897375
11.66667	2.924946
11.73333	2.952517
11.8	2.980088
11.86667	3.007659
11.93333	3.03523
12	3.062801

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

fresh frequency record

frequency (10^14 Hz)	stopping indication (V)
12	3.062801

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

Calculated quantities under the declared measurement model
Quantity	Value	Unit
First calibration indication at frequency eight	1.408534	V
Second calibration indication at frequency ten	2.235668	V
Fitted indicated slope	0.4135668	V per 10^14 Hz
Confounded intercept offset minus work function	-1.9	V
Frozen frequency-twelve prediction	3.062801	V
Fresh frequency-twelve indication	3.062801	V
Independent reference-material indication at ten	1.235668	V
Offset inferred using reference material	0.1	V
Work function conditional on reference calibration	2	eV
Physical threshold frequency conditional on reference	4.835978	10^14 Hz

A line identifies a slope and confounded intercept; an independent material reference separates the work function.

Fit y=m f+c from the first two records. With unit voltage gain, c=B−phi/e, so additional same-offset frequencies do not separate B and phi. The independently known reference work function3 eV supplies B from its own above-threshold indication, then phi=B−c in eV units. The inferred zero of the indicated line is not the physical emission threshold when B is nonzero. Extrapolation below threshold does not predict a negative stopping-energy event.

Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.

A line identifies a slope and confounded intercept; an independent material reference separates the work function.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Define the state, source and evidence

Derive the quantitative relation

Use exactly the first two unknown-material records at frequencies 8 and 10 to fit m=(y10−y8)/2 and c=y8−8m. Reserve frequency 12 before looking at its indication. These records identify m and c=B−phi/e, not B and phi separately. More same-offset frequencies can test linear response but do not remove that parameter ambiguity.

Check normalization, limits and inference

A reference material has independently known work function 3 eV and is observed at frequency 10 with the same offset. Its indication gives B=yref−(10m−3), then the unknown work function in eV is B−c. This added premise breaks the ambiguity. The zero of the indicated line, −c/m, differs from the physical threshold phi/(em) when B is nonzero. No emitted-electron event below threshold follows from extrapolating a negative line value.

Compare a changed premise

Changing intensity above threshold primarily changes electron supply in the simple one-photon model, not the maximum kinetic-energy line. A voltage gain error or frequency calibration error would modify the fitted slope and require another standard. The virtual records are not a physical UV experiment or an independent determination of Planck’s constant.

Worked original case

Investigation

Changed-case practice

Try the changed case before feedback

A fitted intercept is −2.2 V and an independent reference gives offset +0.3 V. Find the unknown work function in eV.

Numerical result in the requested units

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and boundaries

Original derivations and virtual evidence checked 31 October 2026 against the primary explanation. All questions, numerical packets and diagrams are original. These models do not establish actual beam, radiation, vacuum, optical or electrical laboratory performance. Public feedback is practice, not authenticated independent mastery. Preserve first reasoning, criterion critique, revision and a genuinely new assigned packet in the course evidence workspace.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Which state, calibration or boundary premise is independently justified, and what unused observation could distinguish an alternative?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Fit a boost from one record and test unused event differences Next: Derive a wavelength shift from vector momentum and total energy

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