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Química Geral · Nuclear and transition-metal chemistry

Química nuclear

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O que você vai aprender

  • Write and balance nuclear equations for α, β⁻ and β⁺ emission, electron capture, γ emission, bombardment reactions and decay series by conserving mass number and charge.
  • Use the neutron-to-proton ratio and the band of stability to predict whether a nuclide is stable and which decay mode it is likely to follow.
  • Use first-order half-lives to date materials with carbon-14, uranium–lead and potassium–argon data.
  • Calculate mass defects and nuclear binding energies with E = mc², per nucleus, per nucleon and per mole.
  • Explain why fission of heavy nuclei and fusion of light nuclei both release energy, and calculate the energy released from masses.
  • Compare α, β and γ radiation by penetration and biological effect, and use the becquerel, gray and sievert correctly.

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Nuclear notation and balanced equations

A nuclide is written with its mass number A (protons + neutrons) as a left superscript and its atomic number Z (protons) as a left subscript: ²³⁸₉₂U has 92 protons and 238 − 92 = 146 neutrons. Particles get the same treatment, with the charge in the subscript position: α particle ⁴₂He (a helium nucleus, He²⁺, drawn), β⁻ particle (electron) ⁰₋₁e, positron ⁰₊₁e, neutron ¹₀n, proton ¹₁p or ¹₁H, γ ray ⁰₀γ. A nuclear equation is balanced when the superscripts add up to the same total on both sides and so do the subscripts. Example: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He, because 226 = 222 + 4 and 88 = 86 + 2. To find an unknown, subtract: the missing A and Z identify the nuclide, and Z alone fixes the element. Bombardment reactions balance the same way: ¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H (18 = 17 + 1 and 9 = 8 + 1). In a decay series, only α emission changes A (by 4), so the number of α decays is the drop in A divided by 4; the β⁻ decays then make up the difference in Z.

The five common decay modes

α emission removes 2 protons and 2 neutrons: A falls by 4 and Z by 2 (²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He). β⁻ emission turns a neutron into a proton and an ejected electron: A is unchanged and Z rises by 1 (¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e). Positron (β⁺) emission turns a proton into a neutron and an ejected positron: Z falls by 1 (¹¹₆C → ¹¹₅B + ⁰₊₁e). Electron capture (EC) also turns a proton into a neutron, but by absorbing an inner-shell electron, so the electron appears on the left: ⁷₄Be + ⁰₋₁e → ⁷₃Li. Positron emission and EC give the same daughter. γ emission releases energy from an excited nucleus and changes neither A nor Z (⁹⁹ᵐ₄₃Tc → ⁹⁹₄₃Tc + ⁰₀γ). β decays also release a neutrino or antineutrino, which has no charge and practically no mass and is usually left out of general-chemistry equations.

The band of stability

Plotting neutrons (N) against protons (Z) for the stable nuclides gives a narrow band. For light elements (Z up to about 20) stable nuclides have N/Z close to 1 (¹²C, ¹⁶O, ⁴⁰Ca). The ratio rises with Z because extra neutrons are needed to dilute the repulsion between protons: ⁵⁶Fe has N/Z = 30/26 = 1.15 and ²⁰⁸Pb has 126/82 = 1.54. No nuclide with Z ≥ 84 is stable. The position of an unstable nuclide predicts its decay. Above the band (too many neutrons): β⁻ emission lowers N and raises Z. Below the band (too few neutrons): positron emission or electron capture raises N and lowers Z; heavy proton-rich nuclides favour electron capture. Beyond Z = 83: α emission lowers both. A quick test compares the mass number with the element's average atomic mass: sodium is all ²³Na (22.99), so ²⁴Na is neutron-rich and decays by β⁻, while ²²Na is proton-rich and decays by positron emission or EC. Even numbers of protons and neutrons favour stability; most stable nuclides are even–even, and only a handful (²H, ⁶Li, ¹⁰B, ¹⁴N) are odd–odd.

Half-life and radiometric dating

Radioactive decay is first order: N = N₀e^(−kt), k = 0.693/t½, and t = (t½/0.693) × ln(N₀/N). Carbon-14 (t½ = 5730 yr) forms in the upper atmosphere from ¹⁴N + ¹₀n → ¹⁴C + ¹H and enters living things as ¹⁴CO₂ (carbon dioxide, drawn) through photosynthesis and food. While an organism lives, exchange keeps its ¹⁴C/¹²C ratio equal to the atmosphere's; at death the exchange stops and the ¹⁴C decays. Example: living carbon gives 15.3 disintegrations per minute per gram, and a sample gives 4.50. Then t = (5730/0.693) × ln(15.3/4.50) = 8268 × 1.224 = 1.01 × 10⁴ years. Carbon-14 works up to about 50 000 years (roughly nine half-lives); after that too little is left to measure. Rocks are dated with long-lived parents. If a mineral started with no ²⁰⁶Pb and every ²⁰⁶Pb atom came from ²³⁸U (t½ = 4.47 × 10⁹ yr), the original uranium is the uranium left plus the lead formed: N₀ = N(U) + N(Pb).

Mass defect and binding energy

A nucleus weighs less than its separated protons and neutrons. The difference, the mass defect Δm, is the mass equivalent of the binding energy released when the nucleons come together: E = Δm c². Use atomic masses throughout: a ¹H atom (1.007825 u) for each proton, so the electrons cancel, and a neutron (1.008665 u) for each neutron. Using bare proton masses with an atomic mass leaves the electrons unbalanced. Example, ⁴He (4.002602 u): Δm = 2(1.007825) + 2(1.008665) − 4.002602 = 0.030378 u. With 1 u = 931.5 MeV, the binding energy is 0.030378 × 931.5 = 28.30 MeV, about 7.07 MeV per nucleon over 4 nucleons. Per mole, Δm = 3.0378 × 10⁻⁵ kg, so E = 3.0378 × 10⁻⁵ kg × (2.998 × 10⁸ m/s)² = 2.73 × 10¹² J, millions of times larger than chemical bond energies. Binding energy per nucleon is the measure of stability: it rises steeply from ²H (1.11 MeV) to a broad maximum of about 8.8 MeV near ⁵⁶Fe and ⁶²Ni, then falls slowly to about 7.6 MeV for uranium.

Fission and fusion

Any change that moves nuclei toward the peak of the binding-energy curve releases energy. Fission splits a heavy nucleus into two mid-mass fragments: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n, about 200 MeV per fission. Because each fission releases more neutrons than it absorbs, a chain reaction is possible once the fuel exceeds the critical mass, the amount in which, on average, at least one neutron from each fission causes another fission instead of escaping. The fragments keep the high N/Z of uranium (about 1.56), well above the band for their mass, so fission products are β⁻ emitters. Fusion joins light nuclei: ²₁H + ³₁H → ⁴₂He + ¹₀n. With atomic masses, Δm = 2.014102 + 3.016049 − 4.002602 − 1.008665 = 0.018884 u, so 17.59 MeV is released. Per gram of fuel this is about four times the energy of fission. Fusion needs temperatures of about 10⁸ K so that the positively charged nuclei collide fast enough to overcome their electrostatic repulsion.

Radiation, penetration and units

Penetrating power rises α < β < γ: α particles are stopped by a sheet of paper or the outer layer of skin, β particles by a few millimetres of aluminium, and γ rays need several centimetres of lead. Ionizing power runs the other way, so an α emitter such as radon-222 (drawn) is most dangerous when inhaled or swallowed, because all of its energy is deposited in a few cells. Activity counts decays: 1 becquerel (Bq) is one decay per second, and the older curie is 3.7 × 10¹⁰ Bq. Absorbed dose is energy per mass: 1 gray (Gy) = 1 J/kg (100 rad). Equivalent dose, in sieverts (Sv), multiplies the absorbed dose by a radiation weighting factor for biological effect: 1 for β and γ, 20 for α (the rem is 0.01 Sv). So 1 mGy of α radiation counts as 20 mSv, more than 10 mGy of γ radiation (10 mSv).

What to carry forward

Balance every nuclear equation by mass number and by charge. Read the decay mode from the nuclide's place relative to the band of stability: neutron-rich → β⁻, proton-rich → β⁺ or electron capture, Z ≥ 84 → α. Decay is first order, so ages come from t = (t½/0.693) ln(N₀/N). Mass lost becomes energy, E = Δm c² (1 u = 931.5 MeV), and binding energy per nucleon peaks near iron, so both fission and fusion release energy. Bq counts decays, Gy measures energy absorbed and Sv weights it for biological effect.

Problemas de prática (40)

Praticar é grátis com uma conta.

Preveja o produto 6

Nuclear equations

  • Electron capture by beryllium-7Predict the product of electron capture by writing the captured electron as a reactant.
  • Breeding plutonium from uranium-238Follow a neutron capture and two successive β⁻ decays to the final nuclide.
  • Product of radium-226 α decayPredict the daughter nuclide of an α decay by balancing mass number and atomic number.
  • The first artificial transmutationComplete a bombardment equation by finding the particle that balances mass number and charge.
  • Product of strontium-90 β⁻ decayPredict the daughter nuclide of a β⁻ decay from conservation of mass number and charge.

Stability and decay modes

  • Decay modes of sodium-24 and sodium-22Predict the decay modes of a neutron-rich and a proton-rich isotope by comparing each with the stable isotope.

Classificar 4

Nuclear equations

  • What does carbon-11 emit?Identify an emitted particle from the mass-number and charge balance of a decay equation.

Stability and decay modes

  • How does polonium-210 decay?Classify the likely decay mode of a nuclide heavier than bismuth.
  • Which of these nuclides is radioactive?Use even–odd nucleon pairing to pick out the radioactive nuclide among neighbours inside the band of stability.

Fission, fusion and radiation

  • Becquerel, gray and sievertClassify the becquerel, gray and sievert by the quantity each one measures.

Comparar 5

Fission, fusion and radiation

  • Gray versus sievert: α against γCompare the biological effect of two absorbed doses by converting grays to sieverts with radiation weighting factors.
  • Rank radiation by penetrating powerRank α, β and γ radiation by penetrating power and relate it to charge and mass.

Mass defect and binding energy

  • Rank nuclei by binding energy per nucleonRank nuclei by binding energy per nucleon from their total binding energies and mass numbers.

Stability and decay modes

  • Neutron-to-proton ratios along the band of stabilityRank stable nuclides by neutron-to-proton ratio and relate the trend to atomic number.
  • Positron emission and electron capture side by sideCompare positron emission with electron capture by their effect on Z, A and the particles involved.

Calcular 11

Half-life and radiometric dating

  • Radiocarbon age from an activity measurementCalculate a radiocarbon age from the measured ¹⁴C activity per gram of carbon using the first-order decay law.
  • Age of a wooden beam from its carbon-14Find a radiocarbon age when the fraction of carbon-14 left is an exact power of one-half.
  • Potassium–argon age of a volcanic rockCalculate a potassium–argon age, allowing for the fact that only some ⁴⁰K decays produce ⁴⁰Ar.
  • Age of a zircon crystal from its uranium and leadCalculate a mineral's age from a daughter-to-parent atom ratio by reconstructing the original number of parent atoms.

Fission, fusion and radiation

  • Energy from deuterium–tritium fusionCalculate the energy released by a fusion reaction from the mass lost.
  • Energy from fissioning one gram of uranium-235Convert an energy per fission in MeV into the energy released by a macroscopic mass of fuel.
  • Neutrons released in a uranium-235 fissionBalance a fission equation to find how many neutrons are released.

Mass defect and binding energy

  • Binding energy of a helium-4 nucleusCalculate a nuclear binding energy in MeV from atomic masses, keeping electron masses balanced.
  • Binding energy of one mole of helium-4Apply E = Δm c² in SI units to find the nuclear binding energy per mole.
  • Binding energy per nucleon of iron-56Calculate the binding energy per nucleon of a mid-mass nuclide from its atomic mass.

Nuclear equations

  • β⁻ decays from uranium-238 to lead-206Count the β⁻ decays in a decay series from the overall changes in mass number and atomic number.

Encontre o erro 4

Mass defect and binding energy

  • Find the error in a carbon-12 mass defectDiagnose a mass-defect calculation that mixes bare-nucleus particle masses with an atomic mass.

Half-life and radiometric dating

  • Radiocarbon dating a dinosaur?Diagnose the misuse of carbon-14 dating on a sample far older than its useful range.

Stability and decay modes

  • Does gold-198 emit α particles?Diagnose a decay-mode prediction that applies the heavy-element α rule below Z = 84.

Nuclear equations

  • Find the error in an iodine-131 equationDiagnose a β⁻ decay equation in which the atomic number was changed in the wrong direction.

Interprete as evidências 2

Stability and decay modes

  • A nuclide above the band of stabilityRead a nuclide's position on a neutron–proton plot to choose the decay that moves it toward the band of stability.

Mass defect and binding energy

  • Reading the binding-energy curveUse binding energies per nucleon to decide which nuclear changes release energy.

Trabalhe de trás para frente 1

  • Which nuclide gives thorium-234 by α decay?Work backwards from an α-decay daughter to the parent nuclide.

Planeje uma síntese 1

  • Choosing a radiometric clockChoose a dating method by matching the parent nuclide's half-life and occurrence to the sample's age and composition.

Explique por quê 6

Fission, fusion and radiation

  • Why a small piece of uranium-235 does not chain-reactExplain the critical mass in terms of neutrons escaping from the fuel before causing fission.
  • Why fission products emit β⁻ particlesExplain why fission fragments lie on the neutron-rich side of the band of stability and decay by β⁻ emission.
  • Why inhaled radon is dangerousExplain why α emitters are most hazardous when inside the body.

Stability and decay modes

  • Why heavy proton-rich nuclides capture electronsExplain why electron capture competes better with positron emission in heavy proton-rich nuclides than in light ones.

Half-life and radiometric dating

  • Why the carbon-14 clock starts at deathExplain why a living organism keeps a constant ¹⁴C/¹²C ratio while a dead one does not.

Mass defect and binding energy

  • Why is helium-4 lighter than its parts?Explain the mass defect as the mass equivalent of the energy released when nucleons bind.

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