放射線の減衰、レーザーゲインおよびキャビティモード
導入済み| English | 意味 |
|---|---|
| half-value layer/hɑːf ˈvæljuː ˈleɪə/ | 半値層 |
| population inversion/ˌpɒpjʊˈleɪʃn ɪnˈvɜːʃn/ | 粒子数反転 |
A decision before an answer
- A photon beam has no definite range, yet a heavy charged particle does; shielding calculations fail if the two are swapped.
- Your goal: Distinguish charged-particle stopping and range from exponential photon attenuation.
Choose the interaction model
- Heavy charged particles lose energy continuously through many small collisions, so they have an approximate range: under a constant-loss model a particle with initial energy E0 and loss rate dE/dx stops after E0/(dE/dx). Electrons straggle more and radiate.
- Photons instead interact in single events, so a narrow beam attenuates exponentially as I=I0 e^(−μx) with no definite maximum depth; the half-value layer is ln2/μ.
A narrow photon beam passes through three half-value layers. The transmitted fraction is:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Each half-value layer halves the intensity: (1/2)³=1/8.
Attenuate and count
- Apply the exponential only to the stated narrow-beam geometry: μ=0.2 /cm gives a half-value layer of 3.47 cm and I/I0=e^(−2)≈0.135 after 10 cm. Multiply by detector efficiency for recorded counts: with μx=ln4 and ε=0.25 the recorded fraction is 0.25×1/4=1/16.
- Build-up from scattered photons makes broad-beam shielding transmit more than the narrow-beam exponential; state the geometry.
Continuous laser action requires population inversion because in thermal equilibrium:
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Boltzmann populations give N2<N1, so absorption wins without pumping.
Invert the population
- Stimulated emission produces a photon matching the stimulating photon in frequency, direction and phase, giving coherent amplification. It competes with absorption; net gain needs population inversion N2/g2>N1/g1 (N2>N1 for equal degeneracies).
- Positive-temperature equilibrium has N2/g2<N1/g1 by the Boltzmann factor, so a two-level system in equilibrium cannot lase continuously; practical lasers pump a third level or a metastable state.
For μ=0.2 /cm the half-value layer is ln2/0.2=3.47 cm, and three such layers pass 1/8. Under a constant 2 MeV/cm loss model a 5 MeV particle stops after 2.5 cm; a photon beam instead keeps an exponential tail. A 25 cm cavity has mode spacing c/(2L)=600 MHz.
A linear laser cavity of length 25 cm has adjacent longitudinal-mode spacing ____ MHz.
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c/(2L)=3×10⁸/0.5=6×10⁸ Hz=600 MHz.
Resonate in the cavity
- A linear cavity of length L supports standing modes with L=mλ/2, i.e. frequencies ν_m=mc/(2L) with spacing c/(2L): for L=30 cm the spacing is 500 MHz. Gain must exceed the round-trip losses for oscillation.
- Interferometers such as Michelson use the same coherence: fringe counts track optical path changes, as in the gas-cell measurement.
Assigning photons a definite range or charged particles a single exponential law, and forgetting that equilibrium two-level populations cannot invert. Check which interaction model the beam species requires.
このケースに当てはまる答えはどれか？
荷電粒子の停止・到達距離と指数関数的減衰光子の減衰を区別する
Broad-beam shielding transmits exactly the narrow-beam exponential intensity.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Scattered build-up adds transmission; the exponential assumes narrow-beam geometry.
Keep the distinctions
- half-value layer 半值层 — The material thickness that halves an exponentially attenuated beam, equal to ln2/μ.
- population inversion 粒子数反转 — A non-equilibrium state with more population in the upper laser level than the lower, enabling net stimulated emission.
- Distinguish charged-particle stopping and range from exponential photon attenuation.
- Compute attenuated intensity and detected counts with stated coefficients.
- Explain stimulated emission, population inversion and optical cavity resonance conditions.
Match each term with its precise meaning in this lesson.
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Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
難易度 3/5 · 200 コイン + 今日初回完了時に小ボーナス付与
The order follows the stated process; check each stage before the next.