Chapter 10: Nuclear Chemistry – Study Notes

Chapter 10: Nuclear Chemistry

10.1 Introduction to Nuclear Chemistry

Nuclear chemistry focuses on the structure and behavior of atomic nuclei, including the processes by which unstable nuclei change and emit radiation. Understanding atomic number, mass number, and isotopes is foundational to this field.

• Atomic Number (Z): The number of protons in the nucleus of an atom.

• Mass Number (A): The total number of protons and neutrons in the nucleus.

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

• Radioisotopes: Unstable isotopes that spontaneously emit energy to form a more stable nucleus.

• Radioactivity: The emission of nuclear radiation by a radioactive isotope.

10.1B Types of Radiation

Radioactive decay can emit several types of radiation, each with distinct properties and effects.

• Alpha (α) Particles: High-energy particles containing 2 protons and 2 neutrons; charge +2, mass number 4. Symbol: $^4_2\alpha$ or $^4_2\mathrm{He}$.

• Beta (β) Particles: High-energy electrons; charge -1, negligible mass. Symbol: $^0_{-1}\beta$ or $^0_{-1}e$.

• Positrons: Antiparticles of beta particles; charge +1, negligible mass. Symbol: $^0_{+1}\beta$ or $^0_{+1}e$.

• Gamma (γ) Rays: High-energy electromagnetic radiation; no mass, no charge. Symbol: $\gamma$.

Type of Radiation	Symbol	Charge	Mass Number
Alpha particle	$^4_2\alpha$ or $^4_2\mathrm{He}$	+2	4
Beta particle	$^0_{-1}\beta$ or $^0_{-1}e$	-1	0
Positron	$^0_{+1}\beta$ or $^0_{+1}e$	+1	0
Gamma ray	$\gamma$	0	0

10.2 Nuclear Reactions

Nuclear reactions involve changes in the nucleus and are described by nuclear equations. The sum of mass numbers and atomic numbers must be equal on both sides of the equation.

• Radioactive Decay: The process by which an unstable nucleus emits radiation to become more stable.

• Nuclear Equation: $\text{Original Nucleus} \rightarrow \text{New Nucleus} + \text{Radiation Emitted}$

10.2A Alpha Emission

Alpha emission is the decay of a nucleus by emitting an alpha particle. The atomic number decreases by 2 and the mass number by 4.

• Example: $^{241}_{95}\mathrm{Am} \rightarrow ^{237}_{93}\mathrm{Np} + ^4_2\mathrm{He}$

10.2B Beta Emission

Beta emission occurs when a neutron is converted to a proton and a beta particle is emitted. The atomic number increases by 1, mass number remains unchanged.

• Example: $^{14}_6\mathrm{C} \rightarrow ^{14}_7\mathrm{N} + ^0_{-1}e$

10.2C Positron Emission

Positron emission occurs when a proton is converted to a neutron and a positron is emitted. The atomic number decreases by 1, mass number remains unchanged.

• Example: $^{11}_6\mathrm{C} \rightarrow ^{11}_5\mathrm{B} + ^0_{+1}e$

10.2D Gamma Emission

Gamma emission involves the release of energy from a nucleus in the form of gamma rays. There is no change in atomic or mass number.

• Example: $^{99m}_{43}\mathrm{Tc} \rightarrow ^{99}_{43}\mathrm{Tc} + \gamma$

• Gamma emission often accompanies alpha or beta emission.

Summary Table: Types of Nuclear Reactions

Type	Reaction
Alpha emission	$^A_ZX \rightarrow ^{A-4}_{Z-2}Y + ^4_2\mathrm{He}$
Beta emission	$^A_ZX \rightarrow ^A_{Z+1}Y + ^0_{-1}e$
Positron emission	$^A_ZX \rightarrow ^A_{Z-1}Y + ^0_{+1}e$
Gamma emission	$^A_ZX^* \rightarrow ^A_ZX + \gamma$

10.3 Half-Life

The half-life ($t_{1/2}$) of a radioactive isotope is the time required for half of a sample to decay. It is a constant property for each isotope and is independent of sample amount, temperature, and pressure.

• Calculation: After each half-life, half of the remaining radioactive atoms decay.

• Formula: $\text{Remaining Amount} = \text{Initial Amount} \times \left(\frac{1}{2}\right)^n$ where $n$ is the number of half-lives elapsed.

• Example: If the half-life of iodine-131 is 8.0 days, after 32 days (4 half-lives), $100\,\mathrm{mg} \rightarrow 6.25\,\mathrm{mg}$ remains.

Applications of Half-Life

• Radiocarbon Dating: Uses the half-life of carbon-14 to determine the age of carbon-containing materials. Living organisms maintain a constant ratio of C-14 to C-12; after death, C-14 decays and the ratio decreases, allowing age determination.

• Medical and Industrial Uses: Different radioisotopes are used for dating, therapy, and imaging.

Radioisotope	Symbol	Half-Life	Use
Carbon-14	$^{14}_6\mathrm{C}$	$5.70 \times 10^3$ years	Archaeological dating
Cobalt-60	$^{60}_{27}\mathrm{Co}$	5.27 years	Cancer therapy
Iodine-131	$^{131}_{53}\mathrm{I}$	8.02 days	Thyroid therapy
Potassium-40	$^{40}_{19}\mathrm{K}$	$1.25 \times 10^9$ years	Geological dating
Phosphorus-32	$^{32}_{15}\mathrm{P}$	14.3 days	Leukemia treatment
Technetium-99m	$^{99m}_{43}\mathrm{Tc}$	6.01 hours	Organ imaging
Uranium-235	$^{235}_{92}\mathrm{U}$	$7.03 \times 10^8$ years	Nuclear reactors

10.4 Detecting and Measuring Radioactivity

Radioactivity is measured by the number of decays per second. Common units include the Curie (Ci) and the becquerel (Bq).

• 1 Curie (Ci): $3.7 \times 10^{10}$ disintegrations per second

• 1 becquerel (Bq): 1 disintegration per second

• Rad (radiation absorbed dose): Amount of radiation absorbed by 1 gram of substance

• Rem (radiation equivalent for man): Accounts for energy and tissue damage potential

Radiation can damage or kill rapidly dividing cells, making it useful for cancer treatment but also hazardous. Food irradiation uses gamma rays to kill organisms in food, extending shelf life without making the food radioactive.

• Biological Effects: Doses below 25 rem have no detectable effects; 25–100 rem causes temporary white blood cell decrease; >100 rem causes radiation sickness; 500 rem is lethal to 50% of humans (LD50).

10.5 Medical Applications of Radioisotopes

Diagnosis

Radioisotopes are used to diagnose organ function and detect tumors. For example, technetium-99m is used for gall bladder imaging, and thallium-201 for cardiac stress tests.

Positron Emission Tomography (PET)

PET scans use positron-emitting radioisotopes to visualize organ function, detect tumors, and monitor diseases such as Alzheimer's and cancer.

10.6 Nuclear Fission and Fusion

Nuclear Fission

Nuclear fission is the splitting of a heavy nucleus (e.g., uranium-235) into lighter nuclei, releasing energy and neutrons. The released neutrons can initiate further fission, creating a chain reaction. Fission is used in nuclear power plants to generate electricity.

• Critical Mass: The minimum amount of fissionable material needed to sustain a chain reaction.

• Equation Example: $^{235}_{92}\mathrm{U} + ^1_0n \rightarrow ^{91}_{36}\mathrm{Kr} + ^{142}_{56}\mathrm{Ba} + 3^1_0n$

Nuclear Fusion

Nuclear fusion is the joining of two light nuclei (e.g., deuterium and tritium) to form a heavier nucleus, releasing even more energy than fission. Fusion powers the sun but requires extremely high temperatures and pressures, making it currently impractical for energy production on Earth.

• Equation Example: $^2_1\mathrm{H} + ^3_1\mathrm{H} \rightarrow ^4_2\mathrm{He} + ^1_0n$

10.7 Medical Imaging without Radioactivity

Several imaging techniques do not use radioactivity:

• X-rays: Electromagnetic radiation used to image bones and internal organs.

• CT (Computed Tomography) Scans: Use X-rays to create cross-sectional images of the body.

• MRI (Magnetic Resonance Imaging): Uses radio waves and magnetic fields to image soft tissues with minimal cellular damage.