Nuclear Structure, Stability, and Radioactivity

Nuclear Structure and Atomic Composition

Protons, Neutrons, and Atomic Nucleus

The atomic nucleus is the central part of an atom, composed of protons and neutrons. Protons carry a positive electric charge, while neutrons are electrically neutral. The arrangement and number of these particles determine the identity and properties of an element.

• Protons: Positively charged particles found in the nucleus.

• Neutrons: Neutral particles also located in the nucleus.

• Atomic Number (Z): Number of protons in the nucleus; defines the element.

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

Example: Carbon-12 has 6 protons and 6 neutrons ($A = 12$).

Electric Charge and Nuclear Forces

Within the nucleus, protons repel each other due to their positive charges. Neutrons do not participate in this electric interaction, but they play a crucial role in stabilizing the nucleus.

• Electrostatic Repulsion: Protons repel each other via the electric force.

• Nuclear Force: A strong, short-range force that binds protons and neutrons together, overcoming electrostatic repulsion.

• Neutron's Role: Neutrons act as 'nuclear glue,' increasing stability by separating protons and reducing repulsion.

Additional info: The nuclear force is distinct from gravity and electromagnetism, and is mediated by the exchange of particles called mesons at the quantum level.

Nuclear Stability and Instability

Factors Affecting Nuclear Stability

Nuclear stability depends on the ratio of neutrons to protons. As atomic number increases, more neutrons are needed to maintain stability. However, excessive numbers of either can lead to instability.

• Stable Nuclei: Typically have a balanced neutron-to-proton ratio.

• Instability: Occurs when there are too many protons (increased repulsion) or too many neutrons (weakening nuclear force).

• Magic Numbers: Certain numbers of protons and neutrons confer extra stability (e.g., iron is highly stable).

Example: Iron-56 is one of the most stable nuclei. Bismuth-209 is the heaviest stable isotope; heavier nuclei are unstable and radioactive.

Radioactivity and Nuclear Decay

Unstable nuclei undergo radioactive decay to achieve greater stability. This process involves the emission of particles or energy from the nucleus.

• Alpha Decay: Emission of an alpha particle (2 protons, 2 neutrons; identical to a helium nucleus).

• Beta Decay: Emission of an electron (beta particle) from the nucleus, typically when a neutron converts to a proton or vice versa.

• Gamma Decay: Emission of high-energy photons (gamma rays) from the nucleus, usually following other types of decay.

Equations:

• Alpha decay: $^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}He$

• Beta decay: $^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + e^{-}$

Example: Uranium-238 undergoes alpha decay to form Thorium-234.

Nuclear Fission and Fusion

Fission

Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei, accompanied by the release of energy and neutrons. This process is the basis for nuclear reactors and atomic bombs.

• Chain Reaction: Released neutrons can induce further fission events.

• Example: Uranium-235 absorbs a neutron and splits into Barium-141, Krypton-92, and three neutrons.

Equation:

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

Fusion

Nuclear fusion is the process where two light nuclei combine to form a heavier nucleus, releasing energy. Fusion powers stars and has potential for clean energy.

• Example: Two hydrogen nuclei (protons) fuse to form helium.

Equation:

• Fusion: $^{2}_{1}H + ^{3}_{1}H \rightarrow ^{4}_{2}He + ^{1}_{0}n$

Types of Radioactive Decay

Summary Table: Types of Radioactive Decay

The following table summarizes the main types of radioactive decay discussed:

Decay Type	Emitted Particle	Change in Nucleus	Example
Alpha Decay	Alpha particle ($^{4}_{2}He$)	Loss of 2 protons, 2 neutrons	$^{238}_{92}U \rightarrow ^{234}_{90}Th + ^{4}_{2}He$
Beta Decay	Electron ($e^{-}$)	Neutron converts to proton	$^{14}_{6}C \rightarrow ^{14}_{7}N + e^{-}$
Gamma Decay	Gamma photon ($\gamma$)	No change in nucleon number	$^{60}_{27}Co^* \rightarrow ^{60}_{27}Co + \gamma$
Fission	Multiple particles (neutrons, fragments)	Splitting into smaller nuclei	$^{235}_{92}U + ^{1}_{0}n \rightarrow ^{141}_{56}Ba + ^{92}_{36}Kr + 3 ^{1}_{0}n$

Applications and Importance

Radioactivity in Everyday Life

Radioactive decay is fundamental to many applications, including nuclear power generation, medical imaging, and radiometric dating. Understanding nuclear stability and decay is essential for safe handling and technological advancement.

• Nuclear Reactors: Use controlled fission reactions to produce energy.

• Medical Uses: Radioisotopes in diagnosis and treatment.

• Radiometric Dating: Determining the age of materials using known decay rates.

Additional info: The gold foil experiment by Geiger and Marsden provided key evidence for the nuclear model of the atom.