Comprehensive Notes on Nuclear Chemistry

Nuclear Chemistry

Learning Objectives

• Understand the differences between nuclear and chemical changes.
• Identify the three types of radioactive emissions and the types of radioactive decay, and know how each changes $A$ and $Z$.
• Explain how a decay series leads to a stable nuclide.
• Write and balance nuclear equations.
• Use the $N/Z$ ratio to predict nuclear stability and the type of decay a nuclide undergoes.
• Explain the band of stability.
• Define radioactive decay series.
• Predict the relative stabilities of nuclides.
• Understand why radioactive decay is a first-order process and the meaning of half-life.
• Convert among units of radioactivity, and calculate specific activity, decay constant, half-life, and number of nuclei.
• Estimate the age of an object from its specific activity.
• Write the reaction of the nuclear fusion of deuterium and tritium.
• Discuss the pros and cons of power generation by nuclear fission, and evaluate the potential of nuclear fusion.

Recap: Isotopes and Atomic Masses

• All atoms of an element have the same atomic number but not the same mass number.
• Isotopes of an element are atoms with different numbers of neutrons, hence different mass numbers.
• Example: Carbon atoms (Z = 6) have 6 protons and 6 electrons.
  • 98.89% have 6 neutrons (A = 12).
  • 1.11% have 7 neutrons (A = 13).
  • Less than 0.01% have 8 neutrons (A = 14).
• Chemical properties of an element are primarily determined by the number of electrons, thus isotopes have nearly identical chemical behavior despite different masses.

Atomic Number, Mass Number, and Notation

• $X$: Element Symbol
• $A$: Mass Number (number of protons + number of neutrons)
• $Z$: Atomic Number (number of protons)
• $^{A}_{Z}X$
• Examples:
  • Proton: $^{1}<em>{1}H$ or $^{1}</em>{1}p$
  • Neutron: $^{1}_{0}n$
  • Electron: $^{0}<em>{-1}e$ or $^{0}</em>{-1}\beta$
  • Positron: $^{0}<em>{+1}e$ or $^{0}</em>{+1}\beta$
  • Alpha particle: $^{4}<em>{2}He$ or $^{4}</em>{2}\alpha$

Chemical vs. Nuclear Reactions

• Chemical Reactions:
  • Only outer electrons are disturbed; nuclei are not affected.
  • Electrons are shared or transferred to form compounds.
  • Energy changes are relatively small.
  • Rates are influenced by temperature, concentration, and catalysts.
• Nuclear Reactions:
  • Nuclear changes occur, independent of the chemical environment.
  • Nuclei undergo changes, often forming different elements.
  • Electrons are usually bystanders.
  • Energy changes are much greater than in chemical reactions.
  • Rates are affected by the number of nuclei but not by temperature, catalysts, or the compound in which an element occurs.

Comparison of Chemical and Nuclear Reactions (Table 3.1)

Radioactive Decay and Nuclear Stability

• A stable nucleus remains intact indefinitely.
• An unstable nucleus exhibits radioactivity: it spontaneously disintegrates or decays by emitting radiation.
• Each unstable nucleus has a characteristic rate of radioactive decay.
• Types of Nuclear Reactions:
  1. Radioactive Decay: Nucleus spontaneously disintegrates, giving off radiation.
  2. Nuclear Bombardment Reaction: Nucleus is bombarded by another nucleus or nuclear particle. Sufficient energy can cause rearrangement of nuclear particles.
• Nucleons: Protons and neutrons.
• Nuclide: A nucleus with a specific number of protons and neutrons.

Radioactivity Discovery

• Discovered by Antoine Henri Becquerel in 1896.
• Uranium minerals give off radiation that can be separated into alpha ($\alpha$), beta ($\beta$), and gamma ($\gamma$) rays using electric or magnetic fields.

Types of Radioactive Emissions

• Alpha Rays ($\alpha$):
  • Bend toward a negative plate, indicating a positive charge.
  • Consist of helium-4 nuclei (2 protons, 2 neutrons).
• Beta Rays ($\beta$):
  • Bend toward a positive plate, indicating a negative charge.
  • Consist of high-speed electrons.
• Gamma Rays ($\gamma$):
  • Unaffected by electric and magnetic fields.
  • Electromagnetic radiation similar to X-rays but with shorter wavelengths.
• Example: Uranium-238 emits alpha rays and decays to thorium-234.

Types of Radioactive Decay

1. Alpha Emission ($\alpha$):
   • Emission of a helium-4 nucleus from an unstable nucleus.
   • The product nucleus has an atomic number that is two less and a mass number that is four less than the original nucleus.
2. Beta Emission ($\beta$ or \beta^{-}$):
   • Emission of a high-speed electron from an unstable nucleus.
   • Equivalent to the conversion of a neutron to a proton.
   • The product nucleus has an atomic number that is one more than that of the original nucleus; the mass number remains the same.
3. Positron Emission:
   • Emission of a positron from an unstable nucleus.
   • Equivalent to the conversion of a proton to a neutron.
   • The product nucleus has an atomic number that is one less than that of the original nucleus; the mass number remains the same.
4. Electron Capture (EC):
   • Decay of an unstable nucleus by capturing an electron from an inner orbital.
   • In effect, a proton is changed to a neutron, as in positron emission.
   • The product nucleus has an atomic number that is one less than that of the original nucleus; the mass number remains the same.
5. Gamma Emission (\gamma):
   • Emission of a gamma photon from an excited nucleus (metastable nucleus).
6. Spontaneous Fission:
   • The spontaneous decay of an unstable nucleus in which a heavy nucleus (mass number > 89) splits into lighter nuclei and energy is released.
   • Example: Uranium-236.

Nuclear Stability and Radioactive Decay

• Beta Decay:
  • ^{A}{Z}X \rightarrow ^{A}{Z+1}Y + ^{0}_{-1}\beta$</li> <li>Decreases the number of neutrons by 1.</li> <li>Increases the number of protons by 1.</li></ul></li> <li><strong>Positron Decay:</strong><ul> <li>$^{A}{Z}X \rightarrow ^{A}{Z-1}Y + ^{0}_{+1}\beta$</li> <li>Increases the number of neutrons by 1.</li> <li>Decreases the number of protons by 1.</li></ul></li> <li><strong>Electron Capture:</strong><ul> <li>$^{A}{Z}X + ^{0}{-1}e \rightarrow ^{A}_{Z-1}Y$</li> <li>Increases the number of neutrons by 1.</li> <li>Decreases the number of protons by 1.</li></ul></li> <li><strong>Alpha Decay:</strong><ul> <li>$^{A}{Z}X \rightarrow ^{A-4}{Z-2}Y + ^{4}_{2}He$</li> <li>Decreases the number of neutrons by 2.</li> <li>Decreases the number of protons by 2.</li></ul></li> <li><strong>Spontaneous Fission:</strong><ul> <li>$^{A}{Z}X \rightarrow ^{A'}{Z'}Y + … + neutrons$</li></ul></li> </ul> <h4 id="balancingnuclearreactions">Balancing Nuclear Reactions</h4> <ul> <li>The decaying (reactant) nuclide is called the parent; the product nuclide is called the daughter.</li> <li>The total$Z$(charge, number of protons) and the total$A$(sum of protons and neutrons) of the reactants equal those of the products.</li> <li>Nuclear Equation: Symbolic representation of a nuclear reaction.</li> <li>Particles:<ul> <li>$^{1}{1}p$or$^{1}{1}H$: Proton</li> <li>$^{1}_{0}n$: Neutron</li> <li>$^{0}{-1}e$or$^{0}{-1}\beta$: Electron</li> <li>$^{0}{+1}e$or$^{0}{+1}\beta$: Positron</li> <li>$^{4}{2}He$or$^{4}{2}\alpha$: Alpha particle</li></ul></li> </ul> <h4 id="balancingnuclearequationsrules">Balancing Nuclear Equations: Rules</h4> <ol> <li>Conserve mass number ($A$): The sum of protons plus neutrons in the products must equal the sum of protons plus neutrons in the reactants.<ul> <li>Example:$^{235}{92}U + ^{1}{0}n \rightarrow ^{138}{55}Cs + ^{96}{37}Rb + 2^{1}_{0}n$</li> <li>235 + 1 = 138 + 96 + 2(1)</li></ul></li> <li>Conserve atomic number ($Z$) or nuclear charge: The sum of nuclear charges in the products must equal the sum of nuclear charges in the reactants.<ul> <li>Example:$^{235}{92}U + ^{1}{0}n \rightarrow ^{138}{55}Cs + ^{96}{37}Rb + 2^{1}_{0}n$</li> <li>92 + 0 = 55 + 37 + 2(0)</li></ul></li> </ol> <h4 id="examplealphadecayofpolonium212">Example: Alpha Decay of Polonium-212</h4> <ul> <li>$^{212}_{84}Po$decays by alpha emission. Write the balanced nuclear equation.</li> <li>Alpha particle:$^{4}_{2}He$</li> <li>$^{212}{84}Po \rightarrow ^{4}{2}He + ^{A}_{Z}X$</li> <li>$212 = 4 + A$, so$A = 208$</li> <li>$84 = 2 + Z$, so$Z = 82$</li> <li>$^{212}{84}Po \rightarrow ^{4}{2}He + ^{208}_{82}Pb$</li> </ul> <h4 id="conservationlawsinnuclearreactions">Conservation Laws in Nuclear Reactions</h4> <ul> <li>Total charge is conserved (remains constant).</li> <li>Total number of nucleons (protons and neutrons) is conserved (remains constant).</li> </ul> <h4 id="nuclearstabilitythenuclearforce">Nuclear Stability: The Nuclear Force</h4> <ul> <li>The existence of stable nuclei with more than one proton is due to the nuclear force.</li> <li>The nuclear force is a strong force of attraction between nucleons that acts only at very short distances (about$10^{-15}$m).</li> <li>Beyond nuclear distances, nuclear forces become negligible.</li> <li>Inside the nucleus, protons are close enough for the nuclear force to be effective, compensating for electric charge repulsion.</li> </ul> <h4 id="bandofstabilityandnzratio">Band of Stability and N/Z Ratio</h4> <ul> <li>The ratio of the number of neutrons to the number of protons, the$N/Z$ratio, is calculated from$(A - Z)/Z$.</li> <li>For lighter nuclides,$N/Z ≈ 1$is enough for stability.</li> <li>For heavier nuclides to be stable, the number of neutrons must exceed the number of protons.</li> <li>If the$N/Z$ratio is either too high or not high enough, the nuclide is unstable and decays.</li> <li>The band of stability gradually increases from an$N/Z$ratio of 1 (near$Z = 10$) to slightly greater than 1.5 (near$Z = 83$for$^{209}Bi$).</li> <li>The band of stability is the region in which stable nuclides lie in a plot of the number of neutrons vs. the number of protons.</li> </ul> <h4 id="stabilityandnuclearstructuremagicnumbers">Stability and Nuclear Structure: Magic Numbers</h4> <ul> <li>Nuclides with$N$or$Z$values of 2, 8, 20, 28, 50, 82 (and$N = 126$) are exceptionally stable; these are called magic numbers.</li> <li>Magic numbers correspond to the numbers of protons or neutrons in filled nucleon shells.</li> <li>Radioactive nuclei often decay by emitting alpha particles ($^{4}_{2}He$nuclei) due to the special stability of the alpha particle (2 protons and 2 neutrons, both magic numbers).</li> <li>Radioactive decay series often end at stable lead isotopes with 82 protons, a magic number.</li> <li>Some extremely stable nuclides have double magic numbers:$^{4}{2}He$,$^{16}{8}O$,$^{40}{20}Ca$, and$^{208}{82}Pb$($N = 126$).</li> </ul> <h4 id="radioactivedecayseries">Radioactive Decay Series</h4> <ul> <li>All nuclides with atomic number greater than$Z = 83$are radioactive.</li> <li>Natural radioactive elements, such as uranium-238, give a radioactive decay series.</li> <li>A radioactive decay series is a sequence in which one radioactive nucleus decays to a second, which then decays to a third, and so forth, until a stable nucleus (isotope of lead) is reached.</li> <li>Example: Uranium-238 decays by alpha emission to thorium-234, which decays by beta emission to protactinium-234, and so on.</li> </ul> <h4 id="nuclearbombardmentreactionstransmutation">Nuclear Bombardment Reactions: Transmutation</h4> <ul> <li>In 1919, Ernest Rutherford discovered that it is possible to change the nucleus of one element into the nucleus of another by processes controlled in the laboratory.</li> <li>Transmutation is the change of one element to another by bombarding the nucleus of the element with nuclear particles or nuclei.</li> <li>Rutherford bombarded nitrogen nuclei with alpha particles and discovered that protons are ejected in the process:$^{14}N + ^{4}He \rightarrow ^{17}O + ^{1}H$</li> </ul> <h4 id="abbreviatednotationfornuclearbombardmentreactions">Abbreviated Notation for Nuclear Bombardment Reactions</h4> <ul> <li>Example:$^{14}N + ^{4}He \rightarrow ^{17}O + ^{1}H$is abbreviated as$^{14}N(\alpha, p)^{17}O$.<ul> <li>First, write the nuclide symbol for the original nucleus (target).</li> <li>In parentheses, write the symbol for the projectile particle (incoming particle), followed by a comma and the symbol for the ejected particle.</li> <li>After the last parenthesis, write the nuclide symbol for the product nucleus.</li></ul></li> <li>Symbols:<ul> <li>$n$: neutron</li> <li>$p$: proton</li> <li>$d$: deuteron ($^{2}H$)</li> <li>$\alpha$: alpha ($^{4}He$)</li></ul></li> </ul> <h4 id="transuraniumelements">Transuranium Elements</h4> <ul> <li>Transuranium elements are elements with atomic numbers greater than that of uranium ($Z = 92$).</li> <li>Neptunium ($Z = 93$) was produced by bombarding uranium-238 with neutrons.</li> <li>Plutonium ($Z = 94$) was discovered similarly.</li> </ul> <h4 id="rateofradioactivedecayandhalflife">Rate of Radioactive Decay and Half-Life</h4> <ul> <li>Radioactivity is not affected by variables that affect chemical reaction rates.</li> <li>The rate of radioactive decay is proportional to the number of radioactive nuclei in the sample:<ul> <li>$Rate = kN_t$</li> <li>$N_t$is the number of radioactive nuclei at time$t$, and$k$is the radioactive decay constant.</li></ul></li> <li>The rate equation for radioactive decay has the same form as the rate law for a first-order chemical reaction.</li> <li>The SI unit of radioactivity is the becquerel (Bq):<ul> <li>$1 Bq = 1 d/s$(disintegration per second).</li></ul></li> <li>The curie (Ci) is a larger unit:<ul> <li>$1 Ci = 3.70 × 10^{10} d/s$.</li></ul></li> <li>The half-life ($t_{1/2}$) of a nuclide is the time it takes for half the nuclei present in a sample to decay.</li> </ul> <h4 id="radioisotopicdating">Radioisotopic Dating</h4> <ul> <li>Radioisotopic dating uses radioisotopes to determine the age of an object in fields such as art history, archeology, geology, and paleontology.</li> <li>Carbon-14 is present in the atmosphere due to cosmic-ray bombardment.</li> <li>Cosmic rays produce neutrons, which bombard ordinary$^{14}N$atoms to form$^{14}C$:<ul> <li>$^{14}N + ^{1}n \rightarrow ^{14}C + ^{1}H$</li></ul></li> <li>$^{14}C$atoms combine with$O2$, diffuse throughout the atmosphere, and enter the carbon pool as$^{14}CO2$and$H^{14}CO_3^{-}$.</li> <li>Plants take up$CO_2$during photosynthesis, and animals ingest$^{14}C$by eating plants; thus, the$^{12}C:^{14}C$ratio of a living organism is constant.</li> <li>When an organism dies, the$^{12}C:^{14}C$ratio increases as$^{14}C$decays.</li> <li>The difference between the$^{12}C:^{14}C$ratio in a dead organism and the ratio in living organisms reflects the time elapsed since the organism died.</li> </ul> <h4 id="nuclearfissionandfusion">Nuclear Fission and Fusion</h4> <ul> <li><strong>Nuclear Fission:</strong> A heavy nucleus splits into two much lighter nuclei, emitting several small particles at the same time.</li> <li><strong>Nuclear Fusion:</strong> Two lighter nuclei combine to form a heavier one.</li> <li>Both fission and fusion release enormous quantities of energy.</li> <li>The nuclear binding energy is the quantity of energy required to break up 1 mol of nuclei into their individual nucleons.</li> <li>The greater the binding energy per nucleon, the more stable the nuclide.</li> <li>Nuclides become more stable with increasing mass number up to around 60 nucleons and then become less stable with higher numbers of nucleons.</li> </ul> <h4 id="fissionandfusionforincreasedstability">Fission and Fusion for Increased Stability</h4> <ul> <li><strong>Fission:</strong> A heavier nucleus can split into lighter ones (closer to$A = 60$) by undergoing fission, increasing binding energy per nucleon.</li> <li><strong>Fusion:</strong> Lighter nuclei can combine to form a heavier one (closer to$A = 60$) by undergoing fusion, increasing binding energy per nucleon.</li> <li>Hydrogen nuclei fuse to form the very stable helium-4 nucleus.</li> </ul> <h4 id="nuclearfissionchainreaction">Nuclear Fission Chain Reaction</h4> <ul> <li>When a uranium-235 nucleus splits, approximately two or three neutrons are released.</li> <li>If these neutrons are absorbed by other uranium-235 nuclei, these nuclei split and release even more neutrons, leading to a chain reaction.</li> <li>A nuclear chain reaction is a self-sustaining series of nuclear fissions caused by the absorption of neutrons released from previous nuclear fissions.</li> <li>A critical mass is the smallest mass of fissionable material in which a chain reaction can be sustained.</li> <li>An atomic bomb is detonated with a supercritical mass of fissionable material.</li> <li>A nuclear fission reactor is a device that permits a controlled chain reaction of nuclear fissions.</li> <li>Nuclear power plants use nuclear reactors to produce heat, which is used to produce steam to drive an electric generator.</li> <li>Potential hazards include radiation leaks, thermal pollution, and disposal of nuclear waste.</li> </ul> <h4 id="thepromiseofnuclearfusion">The Promise of Nuclear Fusion</h4> <ul> <li>Nuclear fusion is the ultimate source of nearly all the energy on Earth.</li> <li>Deuterium and tritium reaction:<ul> <li>$^{2}H + ^{3}H \rightarrow ^{4}He + ^{1}n$</li> <li>This reaction produces$1.7 × 10^{9}$$ kJ/mol, an enormous quantity of energy with no radioactive by-products.
• Fusion requires enormous energy in the form of heat.
• Nuclear fusion holds great promise as a source of clean abundant energy but requires extremely high temperatures and is not yet practical.