Radioactivity and Nuclear Chemistry: Study Notes

Radioactivity and Nuclear Chemistry

Introduction to Nuclear Chemistry

Nuclear chemistry is the study of the chemical and physical properties of elements as influenced by changes in the nucleus of atoms. Unlike typical chemical processes, nuclear reactions can result in the transformation of one element into another, often accompanied by the emission of significant energy. Radioactivity and nuclear reactions have numerous applications, including medical diagnostics, cancer treatment, and electricity generation.

• Radioactivity is the spontaneous emission of particles or electromagnetic radiation from the nucleus of certain atoms.

• Atoms that emit particles and/or energy from their nucleus are termed radioactive.

• Radioactive decay can result in the formation of a new element (daughter nuclide) from the original (parent nuclide).

• Applications include medical imaging, cancer therapy, and power generation.

Discovery of Radioactivity

The phenomenon of radioactivity was discovered in the late 19th century and has since revolutionized science and medicine.

• Antoine-Henri Becquerel discovered radioactivity in 1896 while studying phosphorescent minerals containing uranium.

• Marie Sklodowska Curie and Pierre Curie continued Becquerel’s work, discovering new elements (polonium and radium) and coining the term radioactivity.

• Radioactivity was found to be a property of certain elements, not just uranium.

Structure of the Nucleus

The nucleus is the central part of an atom, containing protons and neutrons (collectively called nucleons). The arrangement and number of these particles determine the stability and radioactive properties of the atom.

• Protons (symbol: p) have a positive charge.

• Neutrons (symbol: n) are neutral.

• Electrons (symbol: e) have a negative charge and are found outside the nucleus.

• Nuclide: A specific isotope of an element, defined by its number of protons and neutrons.

• Isotopes: Atoms of the same element with different numbers of neutrons.

Types of Radioactive Decay

Radioactive decay occurs when unstable nuclei emit particles or energy to become more stable. The main types of decay are:

• Alpha Decay (α): Emission of an alpha particle (helium nucleus, $^4_2He$). Decreases atomic number by 2 and mass number by 4.

• Beta Decay (β): Emission of a beta particle (electron, $^0_{-1}e$) when a neutron converts to a proton. Increases atomic number by 1; mass number unchanged.

• Gamma Decay (γ): Emission of high-energy photons (gamma rays, $^0_0 ext{γ}$). No change in atomic or mass number.

• Positron Emission (β+): Emission of a positron ($^0_{+1}e$) when a proton converts to a neutron. Decreases atomic number by 1; mass number unchanged.

• Electron Capture: An inner electron is captured by the nucleus, combining with a proton to form a neutron. Decreases atomic number by 1; mass number unchanged.

Example Nuclear Equations

• Alpha decay: $^{224}_{88}Ra \rightarrow ^{220}_{86}Rn + ^{4}_{2}He$

• Beta decay: $^{14}_{6}C \rightarrow ^{14}_{7}N + ^{0}_{-1}e$

• Positron emission: $^{22}_{11}Na \rightarrow ^{22}_{10}Ne + ^{0}_{+1}e$

• Electron capture: $^{76}_{36}Kr + ^{0}_{-1}e \rightarrow ^{76}_{35}Br$

Stability of Nuclei

The stability of a nucleus depends on the ratio of neutrons to protons (N/Z ratio) and the strong nuclear force.

• Strong Force: The force that holds nucleons together, acting only over short distances.

• Stable nuclei have N/Z ratios close to 1 for light elements and up to 1.5 for heavier elements.

• Nuclei with too many neutrons tend to undergo beta decay; those with too few undergo positron emission or electron capture.

• All elements with atomic number (Z) > 83 are radioactive.

Detecting Radioactivity

Radioactive emissions can be detected using specialized instruments.

• Scintillation Counter: Detects flashes of light produced when radioactive rays strike certain chemicals.

• Electroscope: Detects ionization of air caused by radioactive rays.

• Geiger-Müller Counter: Counts electrons generated when argon gas atoms are ionized by radioactive rays.

Radioactive Decay Kinetics

Radioactive decay follows first-order kinetics, meaning the rate of decay is proportional to the number of radioactive nuclei present.

• Rate Law: $\text{Rate} = kN$

• Half-life ($t_{1/2}$): $t_{1/2} = \frac{\ln(2)}{k} = \frac{0.693}{k}$

• Integrated Rate Law: $N_t = N_0 e^{-kt}$

• Radioactive decay is not affected by temperature or chemical environment.

Example Calculation

• If a sample initially contains 1.35 mg of Pu-236 (half-life = 2.86 years), the mass remaining after 5.00 years is calculated using the integrated rate law.

• $k = \frac{0.693}{2.86\ \text{yr}} = 0.2423\ \text{yr}^{-1}$

• $N_t = 1.35\ \text{mg} \times e^{-0.2423 \times 5.00} = 0.402\ \text{mg}$

Radiometric Dating

Radioactive decay is used to determine the age of ancient objects and geological samples.

• Radiocarbon Dating: Uses the decay of carbon-14 ($^{14}C$) to estimate the age of once-living materials. Half-life of $^{14}C$ is 5730 years.

• Uranium-Lead Dating: Uses the decay of $^{238}U$ to $^{206}Pb$ to date rocks and meteorites. Half-life of $^{238}U$ is 4.5 billion years.

Example Table: Radiometric Dating Methods

Method	Isotope	Half-life	Application
Radiocarbon Dating	$^{14}C$	5730 years	Archaeology, paleontology
Uranium-Lead Dating	$^{238}U$	4.5 billion years	Geology, meteorites

Nuclear Fission and Fusion

Nuclear reactions can release enormous amounts of energy by splitting (fission) or combining (fusion) atomic nuclei.

• Fission: A large nucleus splits into two smaller nuclei, releasing energy and neutrons. Used in nuclear power plants and atomic bombs.

• Fusion: Two light nuclei combine to form a heavier nucleus, releasing even more energy per gram than fission. Powers the sun and stars.

• Fission chain reactions require a critical mass of fissionable material (e.g., $^{235}U$, $^{239}Pu$).

• Fusion requires extremely high temperatures and is not yet practical for electricity generation.

Example Fission Reaction

• $^{235}_{92}U + ^{1}_{0}n \rightarrow ^{141}_{56}Ba + ^{92}_{36}Kr + 3 ^{1}_{0}n + \text{energy}$

Transmutation

Transmutation is the process by which atoms of one element are changed into atoms of another element, often by bombardment with particles in a particle accelerator.

• Transmutation disproves Dalton’s atomic theory statement that elements cannot change into other elements.

• Used to create new elements and isotopes, including those not found in nature.

Effects of Radiation on Life

Radiation can damage biological molecules, leading to health risks such as cancer and genetic defects.

• Acute exposure can cause radiation sickness and death.

• Chronic exposure increases cancer risk and may cause genetic mutations.

• The danger of radiation is measured in rems (Roentgen Equivalent Man).

Example Table: Radiation Exposure and Effects

Approximate Dose (rem)	Probable Outcome
0-25	Decreased white blood cell count possible
50-100	Radiation sickness (vomiting, diarrhea)
200-300	Death (within 2 months)
600+	Death (within hours)

Applications of Radioactivity

Radioactivity is widely used in medicine, industry, and research.

• Nuclear Medicine: Uses radioactive tracers for imaging and cancer treatment (e.g., PET scans, brachytherapy).

• Industrial Applications: Measuring thickness, detecting weld defects, sterilizing products.

• Agriculture: Tracing fertilizer use, developing disease-resistant crops.

Summary Table: Types of Radioactive Decay

Decay Type	Particle Emitted	Change in Atomic Number	Change in Mass Number
Alpha (α)	$^4_2He$	-2	-4
Beta (β)	$^0_{-1}e$	+1	0
Gamma (γ)	$^0_0 ext{γ}$	0	0
Positron (β+)	$^0_{+1}e$	-1	0
Electron Capture	None	-1	0

Additional info: Some context and explanations have been expanded for clarity and completeness, including definitions, equations, and applications relevant to a General Chemistry course.