The Atomic Nucleus and Radioactivity: Study Notes

The Atomic Nucleus and Radioactivity

Introduction

This chapter explores the structure of the atomic nucleus, the nature of radioactivity, and the fundamental nuclear processes of fission and fusion. It also covers the strong nuclear force, half-life, transmutation, radiometric dating, and the mass-energy equivalence principle.

Radioactivity

Definition and Origins

• Radioactivity is the process by which unstable atomic nuclei spontaneously transform and emit radiation.

• It results from radioactive decay, a natural process that has existed since before the emergence of humans on Earth.

Unstable Atomic Nuclei

• Unstable nuclei have an imbalance of neutrons to protons.

• Such nuclei are radioactive and will eventually decay to achieve greater stability.

Sources of Radiation

• The majority of radiation encountered is natural background radiation from the Earth and space (cosmic rays).

• Background radiation is more intense at higher altitudes due to increased exposure to cosmic rays.

Cosmic Rays

• Cosmic rays are of two types:

  • High-energy particles (such as protons and atomic nuclei)

  • High-frequency electromagnetic radiation (gamma rays)

• Cosmic rays can transform nitrogen atoms in the atmosphere into radioactive carbon-14, which is incorporated into living organisms.

Radioactive Decay and Element Transformation

• When an atom undergoes radioactive decay, it turns into a completely different element (transmutation).

Types of Radiation

Type	Symbol	Charge	Penetration	Nature
Alpha	α	+2	Low (stopped by paper)	2 protons + 2 neutrons (helium nucleus)
Beta	β	-1	Moderate (stopped by aluminum)	Electron ejected from nucleus
Gamma	γ	0	High (requires thick lead/concrete)	High-frequency electromagnetic wave

• Alpha particles are heavy, positively charged, and cause significant surface damage but are easily stopped.

• Beta particles are lighter, negatively charged, penetrate deeper, and are deflected in the opposite direction to alpha particles in magnetic/electric fields.

• Gamma rays are highly penetrating, have no mass or charge, and are a form of pure energy.

The Atomic Nucleus and the Strong Nuclear Force

Strong Nuclear Force

• The strong nuclear force is a powerful, short-range force that holds protons and neutrons (nucleons) together in the nucleus.

• It is much stronger than the electric repulsion between protons but only acts over very short distances.

• Neutrons help stabilize the nucleus by providing additional strong force attraction without adding repulsive electric charge.

• In large nuclei, nucleons are farther apart, making the strong force less effective and leading to instability.

Half-Life and Transmutation

Half-Life

• Half-life is the time required for half of a radioactive sample to decay.

• It is a constant property for each isotope and is independent of physical or chemical changes.

• The amount remaining after n half-lives is $(1/2)^n$ of the original amount.

Transmutation

• Transmutation is the process of changing one element into another, either naturally (radioactive decay) or artificially (nuclear reactions in laboratories).

• Alpha emission decreases mass number by 4 and atomic number by 2 (element moves two places back in the periodic table).

• Beta emission does not change mass number but increases atomic number by 1 (element moves one place forward).

• Gamma emission does not change mass number or atomic number.

Examples of Transmutation

• Natural: $^{238}_{92}U \rightarrow ^{234}_{90}Th + ^{4}_{2}He$ (alpha decay)

• Artificial: Bombardment of nitrogen with alpha particles produces oxygen and hydrogen.

Radiometric Dating

Principles and Methods

• Radiometric dating uses the known half-lives of isotopes to determine the age of materials.

• Carbon dating is used for organic materials, based on the ratio of carbon-12 to carbon-14 (half-life ≈ 5760 years).

• For rocks and minerals, uranium-lead dating is used (e.g., uranium-238 decays to lead-206).

Example Calculation

• If a sample contains 1/8 the radioactive carbon of a fresh sample, it has undergone 3 half-lives: $3 \times 5760 = 17,280$ years old.

Nuclear Fission

Process and Energy Release

• Nuclear fission is the splitting of a heavy nucleus (e.g., uranium-235) into lighter nuclei, releasing energy.

• Fission is initiated by the absorption of a neutron, causing the nucleus to become unstable and split.

• Energy is released as kinetic energy of the fragments, energy of ejected neutrons, and gamma radiation.

Chain Reactions and Critical Mass

• A chain reaction occurs when the products of one fission event (especially neutrons) trigger further fission events.

• Critical mass is the minimum amount of fissionable material needed to sustain a chain reaction.

• Above critical mass, a self-sustaining and potentially explosive reaction can occur.

Isotopes

• Uranium-235, uranium-238, and uranium-239 are isotopes (same element, different number of neutrons).

• Only uranium-235 is readily fissionable.

Mass–Energy Equivalence: $E = mc^2$

Einstein’s Equation

• Mass and energy are equivalent and interchangeable, as described by $E = mc^2$.

• The energy released in nuclear reactions comes from the conversion of a small amount of mass into energy.

• The mass of a nucleon outside the nucleus is greater than when it is bound inside, due to binding energy.

• Binding energy is the energy required to separate nucleons from the nucleus.

Mass per Nucleon

• Dividing the mass of a nucleus by the number of nucleons gives the mass per nucleon.

• Hydrogen has the greatest mass per nucleon (no binding energy), while iron has the least (most tightly bound).

• Energy is released when moving toward iron in nuclear transformations (fusion of light elements or fission of heavy elements).

Nuclear Fusion

Process and Energy Release

• Nuclear fusion is the combination of light nuclei (e.g., hydrogen) to form heavier nuclei (e.g., helium), releasing energy.

• Fusion requires extremely high temperatures to overcome electrostatic repulsion between nuclei.

• Fusion reactions move nuclei toward iron, the most stable element, releasing energy in the process.

• Fusion is the process that powers stars, including the Sun.

Mass Loss and Energy

• Both fission and fusion result in a loss of mass, which is converted to energy according to $E = mc^2$.

• The total mass of the products is less than the mass of the reactants; the difference is released as energy.

Comparison Table: Fission vs. Fusion

Process	Starting Material	Products	Energy Source	Example
Fission	Heavy nucleus (e.g., U-235)	Lighter nuclei, neutrons	Splitting of nucleus	Nuclear reactors, atomic bombs
Fusion	Light nuclei (e.g., H isotopes)	Heavier nucleus	Combining nuclei	Stars, hydrogen bombs

Additional info: Some explanations and tables have been expanded for clarity and completeness based on standard physics curriculum.