MISSION ATLAS #13 · THE HELIOS INCIDENT — EPISODE 4 (FINALE) · COMPTON SCATTERING
⚖️ RECOIL: The Compton Verdict
Derelict core chamberCompton 1923 · Nobel 1927ONE relationship: Δλ = λc(1−cosθ)

🎯 Learning target

Master ONE relationship — the Compton shift:
Δλ = 2.43 (1 − cos θ) pm, λ′ = λ + Δλ
Forward, inverse (solve for θ), and backward (recover λ) on an unknown source.

⚠️ Misconception to break

"Waves can\u2019t push, and scattered light keeps its wavelength." Classical physics agreed — and was wrong. The photon recoils off an electron like a billiard ball, paying momentum and leaving longer.

🧪 Model & assumptions (stated honestly)

Free, initially-at-rest electron · teaching value λc ≈ 2.43 pm (exact 2.4263) · wavelengths drawn ~10¹¹× larger for viewing (real: picometres) · the electron\u2019s recoil direction is illustrative — its exact formula is another law and stays out of this game · angles are exact.

Difficulty generous tolerances

📐 Key formulas (given)

Compton: Δλ = λc (1 − cos θ), λc = 2.43 pm scattered: λ′ = λ + Δλ (always LONGER) inverse: cos θ = 1 − Δλ/2.43 useful: cos60°=½ · cos90°=0 · cos120°=−½ · cos180°=−1 ceiling: Δλmax = 2λc = 4.86 pm (at 180°)

🏛 Curriculum — 4 exhibits

1️⃣ Billiard Room · Watch — the shift ignores the incoming λ
2️⃣ Cross-Examination · Predict — Δλ and λ′ arm the shot
3️⃣ The Angle Cut · Inverse — the window wants λ′; you aim θ
4️⃣ The Verdict · Crisis — unknown source, 90 s, judgement
Bronze+ seals the next exhibit. Scenarios re-roll every retry.

Controls

Space fire · Enter commit · P pause · R reset exhibit · H hint. Each exhibit opens with a 🧠 reasoning question. Wrong submissions −2 pts.

🏅 How scoring works

Every stage: answer the reasoning question, then compute and commit a number. Your medal is set by accuracy — 🥇 under 5% · 🥈 under 10% · 🥉 under 20% error — and a Bronze or better unlocks the next stage. A wrong answer costs −2 points (−1 on Easy, and your first reasoning slip on each question is free on Easy). A hint costs −3/−4/−5. Fewer tries and higher accuracy mean a higher score — so it always pays to calculate, not guess.
⚖️RECOIL
1/4
Exhibit
0
Score
0
🔥 Streak
0
Wrong
0
Hints
SCATTER CADET
Core chamber tribunal · Dr. Noor Haddad + SPARK
ATLAS #13 · Δλ=2.43(1−cosθ) pm · wrong −2 · hint −3/−4/−5
ATLAS / COURT RECORD

Exhibits

Analysis (precision, not politeness)

✅ Full solution (as on paper)

━ λ′(θ) = λ + 2.43(1−cosθ) · ▲ your number · ▮ window band