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Understanding Nuclear Energy and Isotope Stability in Carbon

Nuclear energy originates from the conversion of mass into energy during isotope stability transformations. For example, when unstable isotopes decay into more stable ones, excess mass is released as energy, as described by Einstein's equation E=mc². This process is observed in various carbon isotopes: C-12 and C-13 are stable, while C-14 is radioactive with a half-life of 5,715 years. The stability of isotopes affects their radioactivity levels, and isotopes with shorter half-lives are generally more radioactive. This complexity can be represented in the "Chart of the Nuclides."

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Understanding Nuclear Energy and Isotope Stability in Carbon

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  1. Answer : The slight excess of mass of the less stable isotopes is converted to energy when isotopes are converted from less stable to more stable ones. Question : Where does nuclear energy come from ? C-11 6P+5N T½=20min M=11.0114 C-9 6P+3N T½=127ms M=9.031 CARBON = C Clue : E = mc2 (COAL, DIAMOND) C-14 6P+8N T½=5715y (from N-14 + n) (~4kBq in 70kg man, none in coal) M=14.0032 C-12 6P+6N STABLE – 18% of body mass M=12.000000 C-12 6P+6N STABLE – 18% of body mass M=12.000000 DNA molecule C-13 6P+7N STABLE – 1.1% of C M=13.0034 C-15 6P+9N T½=2.45s M=15.0106 C-18 6P+12N T½=0.09s M=18.0268 C-22 6P+16N T½=9ms M=22.056 CHEMICAL ELEMENTS & ISOTOPES EXAMPLE: CARBON AND ITS ISOTOPES

  2. TABLE OF ISOTOPES ALSO CALLED “CHART OF THE NUCLIDES” CALCIUM POTASSIUM ARGON CHLORINE SULFUR PHOSPHORUS SILICON NITROGEN ISOTOPES ALUMINIUM MAGNESIUM SODIUM NEON NEON CARBON ISOTOPES CARBON ISOTOPES OXYGEN OXYGEN OXYGEN FLUORINE FLUORINE NITROGEN NITROGEN NITROGEN CARBON CARBON CARBON BORON ISOTOPES BORON BORON BORON CARBON - 12 BERYLLIUM BERYLLIUM BERYLLIUM LITHIUM LITHIUM HELIUM HELIUM HYDROGEN HYDROGEN neutron neutron 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

  3. TABLE OF ISOTOPES ALSO CALLED “CHART OF THE NUCLIDES” Question : What is more radioactive ? A) an isotope with a long half-life ? or B) an isotope with a short half-life ? (assume you have 1 kg of each) Ca 20 NEUTRON-POOR RADIOACTIVE P-35 (T½=47 sec) Si-35 (T½=0.9 sec) Cl-35 (stable) S-35 (T½=87.2 d) K 19 Al-35 (T½=0.03 sec) Ar Clue # 2: Think of radioactive isotopes as a store of energy (like an electric battery) Clue # 1: Think of nuclear radiation as a form of light (high energy form of light) 18 ISOTOPES Mg-35 (T½=0.07 sec) Na-35 (T½=1.5 msec) Cl 17 S DECAY 16 P 15 Si 14 Al 13 Mg 12 NEUTRON-RICH ISOTOPES Na 11 Ne 10 F 9 O 8 N 7 C 6 B 5 Be 4 Li 3 He 2 H 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

  4. Answer : The isotope with a short half-life is more radioactive because all its energy is radiated away quickly !! Clue # 3 Powerful radiation for…. ….one minute ? Little radiation for weeks Identical car batteries – both charged to full

  5. CHEMICAL ELEMENTS & ISOTOPES RADIOACTIVE DECAY Na-35 (T½=1.5 msec) Cl-35 (stable) “VALLEY OF STABILITY” CHART OF THE NUCLIDES – EXCESS MASS Skip next

  6. TABLE OF ISOTOPES ALSO CALLED “CHART OF THE NUCLIDES” URANIUM-235 ( U-235 ) comprises 0.71% of natural uranium (99.28% U-238) (0.006% U-234) Ca 20 K 19 FISSION Ar 18 IRON-56 ( Fe-56 ) Cl OF URANIUM 17 S 16 P 15 Si C-12 14 Al 13 Mg 12 Na 11 Ne 10 F 9 O 8 N 7 C 6 B 5 Be 4 Li 3 He 2 H 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Ba-138 (stable) Cs-138 (T½=32.2 min) Xe-138 (T½=14.1 min) I-138 (T½=6.5 sec) Mo-96 (stable) Nb-96 (T½=23.4 hr) Zr-96 (T½=2x1019 y) Y-96 (T½=6.2 sec) Example : U-235 + n°  Y-96 + I-138 + 2n° (Uranium 235)(Yittrium 96) (Iodine 138)

  7. TABLE OF ISOTOPES IN 3-D CHART OF THE NUCLIDES – EXCESS MASS U-235 Ba-138 (stable) I-138 (T½=6.5 sec) Mo-96 (stable) Y-96 (T½=6.2 sec) U-235 + n°  Y-96 + I-138 + 2n° (Uranium 235)(Yittrium 96) (Iodine 138)

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