[{"data":1,"prerenderedAt":150},["ShallowReactive",2],{"cheatsheet-nuclear-chemistry":3},{"sheet":4},{"sheetSlug":5,"topicSlugs":6,"primaryTopic":7,"title":8,"subtitle":9,"sections":10},"nuclear-chemistry",[5],28,"Nuclear Chemistry","Balancing nuclear equations, decay modes, decay kinetics, binding energy, and fission/fusion.",[11,23,53,88,96,109,117,126,134,142],{"heading":12,"kind":13,"items":14},"Conserve A and Z","rules",[15],{"ref":16,"mode":19,"provenance":20,"text":21,"source_hash":22},{"type":17,"topic":7,"id":18,"field":17},"rule","NC-R001","transform","owned_workbook","Both mass number A (top) and atomic number Z (bottom) are conserved: the sums must match on each side of a nuclear equation.","94d68a5588333e45437978000eaf183350d6c5b95b438f874204ece0a7f5ad0b",{"heading":24,"kind":25,"columns":26,"items":29},"Particles","data",[27,28],"Particle","Symbol (A, Z)",[30],{"ref":31,"mode":19,"provenance":20,"rows":33,"source_hash":52},{"type":17,"topic":7,"id":32,"field":17},"NC-R002",[34,37,40,43,46,49],[35,36],"alpha","⁴₂He (4, 2)",[38,39],"beta-minus","⁰₋₁e (0, −1)",[41,42],"positron","⁰₊₁e (0, +1)",[44,45],"neutron","¹₀n (1, 0)",[47,48],"proton","¹₁p (1, 1)",[50,51],"gamma","⁰₀γ (0, 0)","a793068fc462e68d644b2b7201109d93d7c7fb36869db15fc223c3133c72d5f6",{"heading":54,"kind":25,"columns":55,"items":58},"Decay modes",[56,57],"Mode","Effect on nucleus",[59,66,73,80],{"ref":60,"mode":19,"provenance":20,"rows":62,"source_hash":65},{"type":17,"topic":7,"id":61,"field":17},"NC-R003",[63],[35,64],"A − 4, Z − 2","3b538bc79119aa91e4f825b56fa51cbe1409ce68a5fa31f8888df7200dea7197",{"ref":67,"mode":19,"provenance":20,"rows":69,"source_hash":72},{"type":17,"topic":7,"id":68,"field":17},"NC-R004",[70],[38,71],"A same, Z + 1 (n → p)","f46b3361bb92a816de9ec1fbf74a1d58d831fadd5b299cec1873d0d20bcc3552",{"ref":74,"mode":19,"provenance":20,"rows":76,"source_hash":79},{"type":17,"topic":7,"id":75,"field":17},"NC-R005",[77],[41,78],"A same, Z − 1 (p → n)","e31444733ea9a2483c0927179942f35a081e71716894c063fb1f043854f3d0d7",{"ref":81,"mode":19,"provenance":20,"rows":83,"source_hash":87},{"type":17,"topic":7,"id":82,"field":17},"NC-R006",[84],[85,86],"electron capture","A same, Z − 1 (e⁻ on left)","63cea3daec14ee5711c01d28ec48052d3e819e37f0d1fa9d569c410ec6fc0599",{"heading":89,"kind":13,"items":90},"Multi-step decay counting",[91],{"ref":92,"mode":19,"provenance":20,"text":94,"source_hash":95},{"type":17,"topic":7,"id":93,"field":17},"NC-R007","For x alphas + y betas: solve 4x = mass difference and 2x − y = atomic-number difference simultaneously.","b78e4d9eb9b147dd0f11fc971043fe62cc6c7dfe5c486062a30ff3d52098945e",{"heading":97,"kind":13,"items":98},"Decay kinetics (first order)",[99,104],{"ref":100,"mode":19,"provenance":20,"text":102,"source_hash":103},{"type":17,"topic":7,"id":101,"field":17},"NC-R009","Decay is first-order: k = ln2 / t₁/₂ = 0.693 / t₁/₂ (units of inverse time).","8de4702f921eb34ad04faad1aa972cb76852699225925f93372442a00bdf725a",{"ref":105,"mode":19,"provenance":20,"text":107,"source_hash":108},{"type":17,"topic":7,"id":106,"field":17},"NC-R010","Fraction remaining: N/N₀ = e^(−kt) = (1/2)^(t/t₁/₂). Use the half-life form when t/t₁/₂ is a simple ratio.","677e9c3ea92c2d6efa89bc0eceab503718a5b7460371da36693459cdaf730b83",{"heading":110,"kind":13,"items":111},"Activity & dating",[112],{"ref":113,"mode":19,"provenance":20,"text":115,"source_hash":116},{"type":17,"topic":7,"id":114,"field":17},"NC-R011","Activity is proportional to the atom count, so ln(A/A₀) = −kt substitutes directly, the basis of radiocarbon and other radiometric dating.","e8740d35accb363116fb8d76c3f07b1ce44388e9ca75ce8ed0c25eeea0f1cbf6",{"heading":118,"kind":13,"items":119},"Mass defect & binding energy",[120],{"ref":121,"mode":19,"provenance":123,"text":124,"source_hash":125},{"type":17,"topic":7,"id":122,"field":17},"NC-R012","original","Mass defect Δm = (mass of free protons + neutrons) − (actual nuclear mass). Binding energy BE = Δm·c² (c = 2.998 × 10⁸ m/s).","d8c913cf9b83b09a2d0563261eb037f91b20c85d1d66c58271a18e6902b61734",{"heading":127,"kind":13,"items":128},"Binding energy per nucleon",[129],{"ref":130,"mode":19,"provenance":123,"text":132,"source_hash":133},{"type":17,"topic":7,"id":131,"field":17},"NC-R013","BE/A = total binding energy ÷ A (MeV/nucleon). The curve peaks near iron-nickel (Fe-56 ≈ 8.8 MeV/nucleon), the most stable nuclei.","2f30c6e9c37d2e9b036fae7138d018830d78a94677e4bb38d1cd4802b4da0daf",{"heading":135,"kind":13,"items":136},"Fission vs fusion",[137],{"ref":138,"mode":19,"provenance":123,"text":140,"source_hash":141},{"type":17,"topic":7,"id":139,"field":17},"NC-R014","Fission: a heavy nucleus splits into two mid-mass nuclei + neutrons. Fusion: light nuclei combine. Both release energy when products sit higher on the BE/A curve (toward iron-nickel).","edb58e3e101a430104159deaac9ecd02f499851e1ec57ad9e28444f46bf6ec73",{"heading":143,"kind":13,"items":144},"Activity A = λN",[145],{"ref":146,"mode":19,"provenance":123,"text":148,"source_hash":149},{"type":17,"topic":7,"id":147,"field":17},"NC-R015","Activity A = λN, λ = ln2/t₁/₂, N = number of radioactive atoms (from mass via molar mass and Nₐ). SI unit: becquerel (1 Bq = 1 decay/s).","40082d81252b0e7ae1a4a1a995270f1015d26772d3bdf894a9c24e9797313495",1787246033241]