Separate photon supply from an emission threshold
Light can transfer energy in individual photon events even when its propagation also shows interference. A monochromatic photon has energy hf=hc/λ. For the supplied rounded constant hc=1240 eV nm, a 3 eV photon has wavelength about 413.33 nm. Optical power is energy per time; dividing power by photon energy in joules gives a photon expectation rate. The conversion 1 eV=1.602176634×10⁻¹⁹ J is essential when combining those units.
Learning outcome: Compare energies 1.5,2,2.5 eV at fixed power, then powers 0,1,2 nW at 3 eV. Retain the zero-power and exact-threshold branches separately. Explain why a conditional upper energy bound is not a measured electron event.
Starting recap
Separate per-event energy, expectation rate and measurement indication. Check particle identities, conservation, threshold branches and calibration roles before making a source or detector claim.
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At photon energy 3 eV and power 2 nW, the photon rate is about 4.161006×10⁹ s⁻¹. The supplied yield gives 8.322012×10⁸ collected electrons/s and current magnitude 0.133333 nA. Kmax is 1 eV. Doubling power would double current, not Kmax.
Open the experimentPredict
For this 2 eV work-function model, doubling power at fixed photon energy 3 eV changes:
Experiment
Compare energies 1.5,2,2.5 eV at fixed power, then powers 0,1,2 nW at 3 eV. Retain the zero-power and exact-threshold branches separately. Explain why a conditional upper energy bound is not a measured electron event.
Separate photon energy, photon supply and electron emission
Worked teaching model · synthetic values · Fictitious clean surface with work function 2 eV. Supplied yield 0.2 collected electrons per incident photon only strictly above threshold. At exact threshold zero maximum kinetic energy is an energetic boundary, not a promised current. Zero power means no incident photons. No physical illumination or equipment.
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Photon supply at fixed selected photon energy
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: photon rate, independent of surface threshold (solid). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Photon supply at fixed selected photon energy
photon rate, independent of surface threshold
| incident power (nW) | photon expectation rate (s⁻¹) |
|---|---|
| 0 | 0 |
| 0.05 | 104025000 |
| 0.1 | 208050000 |
| 0.15 | 312075000 |
| 0.2 | 416101000 |
| 0.25 | 520126000 |
| 0.3 | 624151000 |
| 0.35 | 728176000 |
| 0.4 | 832201000 |
| 0.45 | 936226000 |
| 0.5 | 1040250000 |
| 0.55 | 1144280000 |
| 0.6 | 1248300000 |
| 0.65 | 1352330000 |
| 0.7 | 1456350000 |
| 0.75 | 1560380000 |
| 0.8 | 1664400000 |
| 0.85 | 1768430000 |
| 0.9 | 1872450000 |
| 0.95 | 1976480000 |
| 1 | 2080500000 |
| 1.05 | 2184530000 |
| 1.1 | 2288550000 |
| 1.15 | 2392580000 |
| 1.2 | 2496600000 |
| 1.25 | 2600630000 |
| 1.3 | 2704650000 |
| 1.35 | 2808680000 |
| 1.4 | 2912700000 |
| 1.45 | 3016730000 |
| 1.5 | 3120750000 |
| 1.55 | 3224780000 |
| 1.6 | 3328800000 |
| 1.65 | 3432830000 |
| 1.7 | 3536860000 |
| 1.75 | 3640880000 |
| 1.8 | 3744910000 |
| 1.85 | 3848930000 |
| 1.9 | 3952960000 |
| 1.95 | 4056980000 |
| 2 | 4161010000 |
| 2.05 | 4265030000 |
| 2.1 | 4369060000 |
| 2.15 | 4473080000 |
| 2.2 | 4577110000 |
| 2.25 | 4681130000 |
| 2.3 | 4785160000 |
| 2.35 | 4889180000 |
| 2.4 | 4993210000 |
| 2.45 | 5097230000 |
| 2.5 | 5201260000 |
| 2.55 | 5305280000 |
| 2.6 | 5409310000 |
| 2.65 | 5513330000 |
| 2.7 | 5617360000 |
| 2.75 | 5721380000 |
| 2.8 | 5825410000 |
| 2.85 | 5929430000 |
| 2.9 | 6033460000 |
| 2.95 | 6137480000 |
| 3 | 6241510000 |
| 3.05 | 6345530000 |
| 3.1 | 6449560000 |
| 3.15 | 6553580000 |
| 3.2 | 6657610000 |
| 3.25 | 6761630000 |
| 3.3 | 6865660000 |
| 3.35 | 6969690000 |
| 3.4 | 7073710000 |
| 3.45 | 7177740000 |
| 3.5 | 7281760000 |
| 3.55 | 7385790000 |
| 3.6 | 7489810000 |
| 3.65 | 7593840000 |
| 3.7 | 7697860000 |
| 3.75 | 7801890000 |
| 3.8 | 7905910000 |
| 3.85 | 8009940000 |
| 3.9 | 8113960000 |
| 3.95 | 8217990000 |
| 4 | 8322010000 |
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.
| Quantity | Value | Unit |
|---|---|---|
| Photon wavelength using supplied hc | 413.333 | nm |
| Incident photon expectation rate | 4161010000 | s⁻¹ |
| Above work-function threshold | 1 | flag |
| Exact threshold | 0 | flag |
| Collected electron rate under supplied yield | 832201000 | s⁻¹ |
| Collected current magnitude | 0.133333 | nA |
| Energetic upper bound Kmax, conditional on an emitted electron | 1 | eV |
| Power in maximum-energy electrons if all collected electrons reach Kmax | 0.133333 | nW |
Changing power changes photon supply; changing photon energy can cross an emission threshold.
Energy conservation gives Kmax=Ephoton−phi only for an energetically permitted emitted electron. Below threshold the model reports no emitted electrons rather than negative kinetic energy. At exact threshold the available kinetic energy is zero and no finite current is guaranteed. With zero power there are no photons even if the conditional energy bound is positive. The chosen above-threshold yield is a supplied constant, not derived from the energy equation.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
Changing power changes photon supply; changing photon energy can cross an emission threshold.
Energy conservation gives Kmax=Ephoton−phi only for an energetically permitted emitted electron. Below threshold the model reports no emitted electrons rather than negative kinetic energy. At exact threshold the available kinetic energy is zero and no finite current is guaranteed. With zero power there are no photons even if the conditional energy bound is positive. The chosen above-threshold yield is a supplied constant, not derived from the energy equation.
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