# Fotoelektrik Etki Deneyi: verification notes

File: `simulasyonlar/fotoelektrik-etki-deneyi.html`. Tabs: Hikâye · Deney · Millikan · Fizik · Doğrulama. The Doğrulama tab shows **25/25 tests passing**.

## 1. Audit of the original (`kaynak-eski/fotoelektrik.js`, Gemini 2025, React + Recharts)

The app code is at the end of the bundle (byte offset about 587 900). Quoted fragments are de-minified.

| # | Problem | Evidence in the original | Correct physics |
|---|---|---|---|
| 1 | The saturation current depends on electron energy, not on photon flux. | `l = a ? e.I/100*(1-Math.exp(-o/.5))*100 : 0`, where `o` = Ek_max | I_sat = e·η·Φ with Φ = Pλ/(hc), so the current is proportional to optical power. At fixed power, Φ ∝ λ: with constant η, a longer wavelength gives *more* current, up to λ₀. A yield that rises with hν − φ is real near threshold (Fowler 1931: η ∝ (hν − φ)²). The original's 1 − e^(−Ek/0.5 eV) factor is an unlabelled ad-hoc curve that reaches a "100 %" yield and ignores the λ-dependence of the flux. The new version has both a constant-η model and a Fowler model (İleri). |
| 2 | Emission is wrongly gated by the applied voltage. | photon → electron only if `n.canEmit && n.Ek_max_eV >= e.V_applied && Math.random()<.5` | Whether an electron is emitted does not depend on V at all; only whether it is collected does. The condition compares Ek with the *accelerating* voltage. So at V_applied = +2 V with Ek = 0.5 eV, no electrons are emitted, and at any retarding voltage they always are. |
| 3 | The electron acceleration has the wrong sign. | `v = .025 * -e.V_applied * d; t.vx += v*a` | A positive anode attracts electrons. In the original, +V *decelerates* them and −V accelerates them. Combined with #2, at a retarding voltage beyond V_s the animated electrons speed up towards the anode while the I–V plot shows zero current. |
| 4 | The I–V curve is discontinuous at V = 0 and has an unmotivated shape. | `a<=-e ? 0 : a<0 ? t*(1-Math.pow(-a/e,1.5)) : t*(1-.1*Math.exp(2*-a))` | The retarding branch gives I_sat at V → 0⁻, but the accelerating branch gives 0.9·I_sat at V = 0⁺: a 10 % jump. The exponent 1.5 has no physical basis and gives a kink with finite slope at −V_s. Fowler–DuBridge (planar electrodes, T = 0) gives I/I_sat = ((Em + eV)/Em)², which is continuous and reaches zero with zero slope (DuBridge, Phys. Rev. 43, 727 (1933)). |
| 5 | The animated electron energies are inconsistent with the model's own curve. | `n.Ek_max_eV*(.8+.2*Math.random())` | All electrons are drawn within 20 % of Ek_max, yet the I–V curve implies a broad distribution. Now: normal energies are sampled from dN/dE ∝ (Em − E), the same distribution that produces the I–V curve (tested). |
| 6 | Work functions are unsourced textbook values; Pt is outside the measured range. | `Na 2.28, Zn 4.33, Cu 4.7, Cs 2.1, Pt 6.35` | These match textbook tables (HyperPhysics / Tipler; Serway / OpenStax list Pt 6.35, Cu 4.70). CRC Handbook polycrystalline photoelectric values are Na 2.36, Cs 1.95, Zn 3.63 and Pt 5.64 (faces 5.12–5.93), with Cu 4.65 (Michaelson 1977). Pt 6.35 lies outside every CRC value. Na 2.28 is close to CRC 2.36 and is not really "wrong". No caveat about surface or crystal-face dependence was given. |
| 7 | UV light is invisible. | the colour function `Hg` returns `[0,0,0]` for λ < 380 nm, drawn on `#0A0F1E` | The wavelength slider goes down to 200 nm, but below 380 nm the light cone and photons are black on a near-black background. Now: UV is drawn as a dashed neutral grey beam labelled "UV, görünmez". |
| 8 | The emission probability is presented without scale. | `Math.random()<.5` | Real metals have η ≈ 10⁻⁵ to 10⁻³ (Cu(111): 1.06 × 10⁻⁴ at 260 nm, Greaves et al., FEL2011 THPB15). Each dot is now labelled as representing many electrons, and η = 10⁻³ is stated. |
| 9 | The stopping voltage is identified with Ek_max with no mention of contact potential. | `v_stop_V: i` (= Ek_max) | This is fine as an idealisation, but the measured value is eV_s = hν − φ_*collector*. It is now modelled at İleri level (copper-anode option). |
| 10 | Minor issues. | intensity slider min 10 %; current axis label "göreli"; no classical contrast, no time-lag discussion, no h measurement | All three are now central to the new version. |

The original's "Fiziksel Değerler" panel was correct for the ideal formulas: E = hf, Ek = hf − φ, f₀ = φ/h. Its constant h = 4.135667696e-15 eV·s is the exact h/e.

## 2. What the new version models

All formulas are small pure functions in the second `<script>` block.

- **Photon energy:** E = hc/λ (`photonE`). Mercury-line energies use vacuum wavelengths, while labels show air wavelengths (NIST ASD).
- **Einstein:** Ek,max = hν − φ, ν₀ = φ/h, λ₀ = hc/φ (`ekMax`, `thresholdHz`, `thresholdNm`).
- **Flux and current:**
  - Φ = Pλ/(hc) (`photonFlux`).
  - I_sat = e·η·Φ (`iSat`). The constant-η model uses η = 10⁻³; the Fowler (T = 0) model uses η = 10⁻³·(hν − φ)²/eV².
  - Lab power: 0–10 µW on 1 cm². In the Millikan tab each Hg line gives 1 µW after filtering.
- **Retarding curve (Fowler–DuBridge, T = 0, parallel plates):** I(V) = I_sat·((Em + eV_eff)/Em)² for −Em ≤ eV_eff ≤ 0. It is 1 above that range and 0 below. Em = hν − φ (`retardFrac`, `current`).
- **Contact potential (İleri):** V_eff = V − (φ_A − φ_K)/e, so eV_s = hν − φ_A (`stopV`). The anode option is Cu, 4.65 eV.
- **Tube animation:**
  - Normal energies are sampled by inverse transform, E_n = Em(1 − √u).
  - Motion is under constant acceleration a ∝ V_eff in normalised gap units, with v ∝ √E so that ½mv² is consistent.
  - Electrons turn back where E_n = e|V_eff|x.
  - Below threshold nothing is emitted at any intensity, and emission starts with no delay.
- **Classical expectation mode:**
  - The light is drawn as continuous wavefronts.
  - The accumulation time is t = φ/(I·πr²) with r = 1 Å (`classicalTime`). This gives about 2 min for Na at 100 % and about 20 min at 10 %. The animation runs 60× faster.
  - After the accumulation time, electrons are emitted at any wavelength with Ek ∝ intensity. The scale (3 eV at 100 %) is arbitrary and labelled as qualitative.
  - A live comparison table sets the classical expectation against the observation.
- **Millikan tab:**
  - Measured values of V_s are fitted by least squares: slope h/e → h, intercept → φ (or φ_anode).
  - Two measurement methods are available:
    1. **Zero current.** The ammeter has a 0.1 pA floor, so the measured value is V_s(1 − √(I_det/I_sat)). This gives h about 2.3 % low for Na, which is a real and explained bias.
    2. **√I linear extrapolation (İleri).** This is unbiased in this model.
  - The "Elle kaydet" button lets students record their own slider reading.
- **Work functions (eV):** Cs 1.95, K 2.29, Na 2.36, Zn 3.63, Cu 4.65, Pt 5.64. The reported ranges are shown in the Fizik tab.
- **Parameter ranges:** λ 200–750 nm (as in the original), V −5 to +5 V (Millikan tab −3 to +1 V, or ±3 V with contact potential), intensity 0–100 %.

## 3. Verification table (all pass, 25/25)

| Test | Expected | Model | Source |
|---|---|---|---|
| Millikan-line slope from the model's own V_s (Cs, 7 Hg lines) | h/e = 4.135667696 × 10⁻¹⁵ V·s | 4.1356677 × 10⁻¹⁵ | CODATA 2018 (exact); residual 3 × 10⁻⁹ from rounding of hc in eV·nm |
| Intercept → φ (Cs) | 1.95 eV | 1.9500 | analytic |
| λ₀ for Cs, K, Na, Zn, Cu, Pt (6 tests) | 635.82, 541.42, 525.36, 341.55, 266.63, 219.83 nm | same (≤ 0.0012 %) | λ₀ = 1239.842/φ, computed by hand |
| Hg 253.65 nm photon energy | 4.8865 eV (6s6p ³P₁ = 39 412.300 cm⁻¹) | 4.8865 | NIST ASD; same level as Franck–Hertz 4.9 V |
| Ek,max for Na at 253.65 nm | 2.5265 eV | 2.5265 | hν − φ |
| Photon flux, 1 mW at 405 nm | 2.0388 × 10¹⁵ s⁻¹ | 2.0388 × 10¹⁵ | Pλ/(hc), computed by hand |
| I_sat linearity, I(2P)/I(P) and I(10P)/I(P) | 2, 10 | 2, 10 | Lenard 1902; I = eηΦ |
| Fixed power, I(500 nm)/I(250 nm) | 2 | 2 | Φ ∝ λ |
| No current below threshold (Na, λ = 1.001 λ₀, 1 µW to 1 kW, −5 to +100 V) | 0 in 16 cases | 0 | Einstein 1905 (single-photon) |
| I–V continuity at V = 0 and −V_s | continuous | continuous | the original had a 10 % jump |
| Mean normal energy ⟨E⟩/Em of the sampler | 1/3 | 0.33333 | analytic, triangular distribution |
| Retarding fraction at −V_s/2 vs sampler | 1/4 | 0.2500 | Fowler–DuBridge |
| √I extrapolation recovers V_s (Na, 312.57 nm) | 1.6055 V | 1.6055 | analytic |
| Zero-current bias (0.1 pA floor) | V_s(1 − √(I_det/I_sat)) = 1.5735 V | 1.5735 | analytic |
| Contact potential: intercept = φ_anode (Cs/Cu) | 4.65 eV | 4.6500 | eV_s = hν − φ_A |
| Millikan 1916 sodium slope h/e | 4.1357 × 10⁻¹⁵ | 4.128 × 10⁻¹⁵ (0.19 %) | Millikan, Phys. Rev. 7, 355, p. 375 |
| Millikan 1916 h = 6.57 × 10⁻²⁷ erg·s | 6.626 × 10⁻³⁴ J·s | 6.57 × 10⁻³⁴ (0.85 %) | p. 388; see the note below |
| Millikan slope × modern e | 6.6261 × 10⁻³⁴ | 6.6138 × 10⁻³⁴ (0.19 %) | — |
| Classical accumulation time, 1 W source at 1 m, r = 1 Å, φ = 2.1 eV | ≈ 1.4 × 10² s | 135 s (3.9 %, the book rounds) | Eisberg & Resnick (1985), Example 2-1 |

**Real discrepancy, explained rather than hidden.** Millikan quoted h = 6.57 × 10⁻²⁷ erg·s "with a precision of about .5 per cent". It is 0.85 % below today's value. Almost all of the gap comes from his own value of e, 4.774 × 10⁻¹⁰ esu (p. 374), which is about 0.6 % low because of his air-viscosity value. Multiplying his measured slope by the modern e leaves a 0.19 % difference. The test tolerance (1.2 %) is set to show this, and the note explains it.

## 4. Historical claims with sources

- **Hertz 1887.** *Ann. Phys. Chem.* 31 (267), 983. UV from the primary spark eases the secondary spark. Glass and mica block it; quartz (rock crystal) transmits. The effect is strongest near the negative pole.
- **Hallwachs 1888.**
  - *Ann. Phys. Chem.* 33, 301: zinc plate with a gold-leaf electroscope and an arc lamp. A negative plate lost about 70 % in 5 s at 70 cm. A positive plate lost only about 10 % in 60 s, so I wrote "barely" rather than "not at all".
  - *Ann. Phys. Chem.* 34, 731: neutral plates charge positive, a little over 1 V for Zn.
- **J. J. Thomson 1899.** *Phil. Mag.* 48, 547. e/m of the UV carriers is 7.3 × 10⁶ emu, "of the same order" as cathode rays. Lenard, *Ann. Phys.* 2, 359 (1900), made a better measurement.
- **Lenard 1902.** *Ann. Phys.* 8, 149.
  - "Es sind aber die Grössen der Anfangsgeschwindigkeiten unabhängig von der Intensität des Lichtes" is translated in the text.
  - Arc intensity was varied about 70× with less than 1 % change.
  - He did *not* find the frequency dependence (Millikan 1916, p. 356). The text says "ışık türü".
  - The "trigger" idea is paraphrased from his "nur eine auslösende Rolle"; the noun "Auslösungshypothese" is not used.
- **Einstein 1905.** *Ann. Phys.* 17, 132. Dated Bern, 17 March 1905; received 18 March 1905 (the scan shows both). The text calls it a "sezgisel bakış açısı", following the paper's title ("heuristischen Gesichtspunkt").
- **Nobel prizes (nobelprize.org).**
  - Einstein, 1921 prize awarded in 1922: "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".
  - Millikan, 1923: "for his work on the elementary charge of electricity and on the photoelectric effect".
- **Millikan 1914 and 1916.**
  - *Phys. Rev.* 4, 73 (1914); *Phys. Rev.* 7, 355 (1916).
  - "Machine shop in vacuo" (p. 361).
  - Sodium and lithium data; potassium was lost to an accident.
  - Contact EMF measured in vacuo by the Kelvin method (p. 363).
  - Skepticism, verbatim on p. 383: "the semi-corpuscular theory by which Einstein arrived at his equation seems at present to be wholly untenable".
  - Classical estimate on pp. 384–385: a candle at 3 m and a 10⁻¹⁵ cm² target need at least 12 000 s (4 h).
  - His sodium emitted even at 5461 Å. With the contact correction he put its threshold near 6800 Å and said the limit "is by no means a constant" (pp. 380–381). This is mentioned at İleri level in the Millikan tab.
- **Millikan 1949 quote** ("I spent ten years of my life testing that 1905 equation…"). It is widely attributed to *Rev. Mod. Phys.* 21, 343 (1949), but I could not verify the wording against the primary text, so **it is not used on the page**.
- **Lawrence & Beams 1928.** *Phys. Rev.* 32, 478 (September 1928, not 1927). Emission begins in less than 3 × 10⁻⁹ s.
- **Eisberg & Resnick (1985), Example 2-1.** Potassium, 1 W source at 1 m, r = 1 Å, 2.1 eV, giving about 1.4 × 10² s.
- **Richardson & Compton 1912 and Hughes 1913.** *Phil. Mag.* 24, 575 and *Phil. Trans. A* 212, 205. Used in the timeline as "approximately linear".
- **Lamb & Scully 1969.** "The photoelectric effect without photons", in *Polarisation, Matière et Rayonnement* (PUF). Authors, title, publisher and year are confirmed via NASA NTRS; the page numbers (363–369) are not, so they are omitted.
- **Kimble, Dagenais & Mandel 1977.** *Phys. Rev. Lett.* 39, 691. Cited from my own knowledge and not re-checked online in this session; it is standard.
- **Work functions.**
  - CRC Handbook, "Electron Work Function of the Elements": current edition, photoelectric values via a reproduction of the HBCP table.
  - Michaelson, *J. Appl. Phys.* 48, 4729 (1977), for Cu 4.65 and the upper ends of the ranges.
- **Hg lines.** NIST ASD air wavelengths 253.652, 312.567, 365.016, 404.656, 435.834, 546.075, 576.961 nm. Vacuum wavelengths were converted with the Edlén formula.

## 5. Known limitations

- **Geometry.** Ideal planar electrodes, so saturation is reached at V_eff = 0. Real tubes with a cylindrical cathode and a wire anode need a few volts. Space charge, reflectivity, surface states, the Schottky effect and stray light are not modelled.
- **Temperature.** T = 0 Fowler–DuBridge. The thermal tail (kT ≈ 0.026 eV) beyond −V_s and just below threshold is described in the İleri text but not drawn. This keeps the "nothing below threshold" message exact.
- **Yield.** η = 10⁻³ and the Fowler coefficient are illustrative. The Fowler law only holds near threshold.
- **Classical mode.** The scale of the Ek ∝ intensity line is arbitrary (labelled as such). The accumulation time uses a geometric cross-section; a resonant cross-section (≈ λ²) would shorten it and is mentioned in the text.
- **Millikan tab.** Every Hg line gives the same filtered power (1 µW). Real line strengths differ and filter leakage is ignored. Measurements have no random noise; only the detector floor creates the bias.
- **Animation.** Not to scale. Electrons cross in about 1 s instead of about 1 ns, and each dot stands for many electrons.

## 6. Core-template changes

No changes were made to the core `<style>` or `Q4` script blocks. Three template issues are worth merging back:

1. **`box-sizing` inside `<details>`.** Children of `<details>` are slotted through a UA shadow-DOM slot, so the `*{box-sizing:inherit}` chain breaks and they become `content-box`. Every `.ctl select` inside `details.settings` overflowed its panel by about 15 px. I fixed it in the sim-specific CSS with `details > *{box-sizing:border-box}`. Suggested core fix: add the same rule (or use `box-sizing:border-box` on `*` directly).
2. **`Q4.canvas` does not clear before redrawing.** `cv.redraw` calls `draw()` without `clearRect`, so any canvas that is redrawn (animations, slider updates) accumulates strokes unless every draw function clears itself. I clear at the top of each draw function. Suggested core fix: `ctx.clearRect(0,0,cv.w,cv.h)` inside `cv.redraw` before `draw`.
3. **Minor:** `Q4.frame` scales `pad.l` and `pad.b` with projection mode but not `pad.r` or `pad.t`.