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Decay Analysis of Be-8, C-14, and L-Decay: Energy and Momentum Conservation

This document analyzes the decay processes of Beryllium-8 (Be-8) and Carbon-14 (C-14), examining the calculations for excess mass, released energy, kinetic energy, and momentum conservation. Detailed equations provide insight into how energy is conserved during decays, with a focus on the mass-energy equivalence principle (E=mc²). The analysis also includes the decay of L-particles, incorporating both theoretical and experimental perspectives. Understanding these decay processes is crucial for fields such as nuclear physics and particle physics.

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Decay Analysis of Be-8, C-14, and L-Decay: Energy and Momentum Conservation

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  1. Be8 Decay Mass Be8 = 8.005305 u Excess mass = 9.9x10-5 u Mass He4 = 4.002603 u Ereleased = Dmc2 = (9.9x10-5 u) c2 (931.5 MeV/c2 / u) = .0922 MeV p1 p2 Momentum conservation: Energy conservation: Constituent equations:

  2. Be8 Decay (continued) Energy Be8 = (8.005305 u) c2 (931.5 MeV/c2 / u) = 7456.94 MeV Energy He4 = 7456.94 MeV/2 = 3728.47 MeV Rest energy He4 = (4.002603 u) c2 (931.5 MeV/c2 / u) = 3728.42 MeV Kinetic energy He4 = 3728.47 - 3728.42 MeV = .05 MeV Momentum = Sqrt[E2/c2 –m2c2] = 19.3 MeV/c Classical kinetic energy = p2c2/(2 mc2) = .05 MeV g = 1.000013 b = .0052

  3. C14 Decay N14+ pe pn Mass C14 = 14.003242 u = 13044.020 MeV Mass N14 = 14.003074 u = 13043.863 MeV Mass e- = .511 MeV Mass N14+ = Mass N14 - Mass e- = 13043.352 MeV Excess Energy = .668 MeV Momentum conservation: Energy conservation: Constituent equations:

  4. C14 Decay (continued)

  5. C14 Decay – Fastest Electron n pe pN Momentum conservation: Energy conservation: Constituent equations:

  6. L Decay L pp pp Mass L = 1115.6 MeV Center of mass Mass p- = 139.6 MeV Mass p = 938.6 MeV Momentum conservation: Energy conservation: Constituent equations:

  7. L Decay Solved in Lab pp L pp Mass p = 938 MeV Mass p- = 139.6 MeV Momentum conservation: Energy conservation: Constituent equations: Mathematica solution

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