Nuclear Physics: Structure, Decay, Half-Life, and Induced Reactions

Comprehensive practice flashcards defining core vocabulary, processes, equations, and diagrams across nuclear structure, radioactive decay modes, half-life kinetics, and induced nuclear reactions.

Nucleons

The collective term for protons and neutrons located within the central nucleus of an atom, possessing nearly equal masses of $1.673 \times 10^{-27}\,\text{kg}$ and $1.675 \times 10^{-27}\,\text{kg}$ respectively.

Atomic Number ($Z$)

The total number of protons present in the nucleus of an atom, defining the identity and chemical properties of an element.

Neutron Number ($N$)

The total number of neutrons contained within an atomic nucleus, calculated by subtracting the atomic number from the mass number ($N = A - Z$).

Mass Number ($A$)

The total number of nucleons (protons plus neutrons) in an atomic nucleus ($A = Z + N$), which approximately equals the total mass of the nucleus.

Nuclide

A specific species of an atomic nucleus characterised by its number of protons and neutrons, commonly represented in standard nuclear notation as ${}^{A}_{Z}\text{X}$.

Isotopes

Atoms of the same element that share the same atomic number ($Z$) and identical electron configurations but possess different mass numbers ($A$) due to varying numbers of neutrons, resulting in identical chemical properties but different physical properties (such as melting and boiling points).

Strong Nuclear Force

A powerful, charge-independent, short-range attractive force that binds nucleons together in the nucleus, counteracting the electrostatic Coulomb repulsion between positively charged protons.

Range of the Strong Nuclear Force

The distance thresholds over which the strong nuclear interaction operates: it is strongly attractive between $0.5\,\text{fm}$ and $1.25\,\text{fm}$, rapidly falls to zero beyond approximately $2\text{--}3\,\text{fm}$, and becomes repulsive at distances less than $0.5\,\text{fm}$ to prevent nucleons from merging.

Nuclear Stability Limit

The physical threshold beyond which no stable nuclei can exist, occurring at an atomic number $Z > 83$ and a mass number $A > 209$; any nuclide exceeding these values is inherently radioactive and unstable.

Mass Defect ($\Delta m$)

The difference between the total calculated mass of a nucleus's individual constituent nucleons and the actual, lower mass of the bound nucleus: $\Delta m = (Z\,m_p + N\,m_n) - m_{\text{nucleus}}$.

Binding Energy ($E$)

The energy required to disassemble a nucleus into its constituent nucleons, equivalent to the mass defect converted to energy via Einstein's mass-energy equivalence relation: $E = \Delta m\,c^2$, where $c = 3 \times 10^8\,\text{m/s}$.

Radioactive Decay

The spontaneous process wherein an unstable parent nucleus emits particles and/or electromagnetic radiation to shift its neutron-to-proton ratio toward the band of stability, yielding a daughter nucleus.

Alpha Decay ($\alpha$)

A type of radioactive decay typical of heavy nuclei ($Z > 83$) in which the nucleus emits an alpha particle (${}^4_2\text{He}$), reducing its atomic number by $2$ and mass number by $4$: ${}^A_Z\text{X} \rightarrow {}^{A-4}_{Z-2}\text{Y} + {}^4_2\text{He}$.

Beta Minus Decay ($\beta^-$)

A decay occurring in nuclei with an excess of neutrons relative to protons (left of the stability line), where a neutron converts into a proton, emitting an electron (${}^0_{-1}\text{e}$) and an electron antineutrino ($\bar{\nu}$): ${}^1_0\text{n} \rightarrow {}^1_1\text{p} + {}^0_{-1}\text{e} + {}^0_0\bar{\nu}$.

Beta Plus Decay ($\beta^+$)

A decay occurring in nuclei with an excess of protons relative to neutrons (right of the stability line), where a proton converts into a neutron, emitting a positron (${}^0_{+1}\text{e}$) and an electron neutrino ($\nu$): ${}^1_1\text{p} \rightarrow {}^1_0\text{n} + {}^0_{+1}\text{e} + {}^0_0\nu$.

Positron (${}^0_{+1}\text{e}$)

The antimatter counterpart of an electron, possessing the same mass as an electron but a positive unit charge ($+1$), emitted during beta plus decay.

Gamma Decay ($\gamma$)

The emission of high-energy electromagnetic gamma rays from an excited nucleus (${}^A_Z\text{X}^* \rightarrow {}^A_Z\text{X} + n\gamma$) returning to a lower energy state or ground state, frequently following alpha or beta decay.

Decay Series

A sequential succession of radioactive decays that an unstable parent nucleus undergoes through multiple intermediate daughter nuclides until reaching a stable, non-radioactive isotope.

Ionising Radiation

Particles or electromagnetic waves possessing sufficient energy to strip electrons from atoms and molecules, producing ions, breaking chemical bonds, and causing tissue damage or cellular mutations.

Penetrating Power of Radiation

The ability of radioactive emissions to pass through matter, which is inversely proportional to ionising ability: alpha particles are stopped by a sheet of paper, beta particles penetrate paper but are absorbed by aluminum, and gamma rays penetrate deeply, requiring thick lead for shielding.

Half-Life ($t_{1/2}$)

The time required for half of the radioactive nuclei in a given sample to decay, which is strictly constant for a particular radioisotope and entirely independent of physical or chemical conditions ($t_{1/2} = \frac{\ln(2)}{\lambda}$).

Decay Constant ($\lambda$)

A characteristic proportionality constant of an isotope representing the probability per unit time that a nucleus will decay, governing the rate in $N = N_0\,e^{-\lambda\,t}$.

Radioactive Activity ($R$)

The number of radioactive disintegrations occurring per second in a sample, expressed in units of Becquerels ($\text{Bq}$) and calculated via the exponential decay equation $R = R_0\,e^{-\lambda\,t}$.

Radiometric Dating

A technique that estimates the age of geological or biological materials by determining the relative proportions of radioactive parent isotopes and their decay products based on known decay rates.

Carbon-14 Dating

A radiometric dating method for organic remains based on the beta minus decay of Carbon-14 ($t_{1/2} = 5730\,\text{years}$) into Nitrogen-14; because carbon uptake ceases upon death, the ratio of residual Carbon-14 to stable Carbon-12 reveals the time elapsed since death.

Low-Level Waste (LLW)

Radioactive refuse comprising small quantities of radioactive substances with relatively short half-lives (e.g., contaminated protective clothing, rags, and equipment), typically encased in lead-lined steel drums and stored in shallow land burials.

High-Level Waste (HLW)

Highly radioactive materials with long half-lives generated as reactor by-products (such as spent fuel rods, liquid extracts, and sludges), requiring containment in heavy metal canisters lined with concrete and stored deep underground.

Induced Nuclear Reaction

A nuclear transformation stimulated by bombarding a target nucleus with energetic particles (such as slow neutrons) rather than proceeding spontaneously.

Nuclear Fission

The division of a heavy, unstable atomic nucleus into two lighter fission fragments (daughter nuclei) along with $2$ to $4$ free neutrons and energy liberated from the mass difference: $E = \Delta m\,c^2$.

Chain Reaction

A self-sustaining progression of nuclear fissions occurring when the free neutrons released by one fission event induce further fissions in neighbouring fissile nuclei.

Control Rods

Rods manufactured from strong neutron-absorbing materials (such as cadmium) that are inserted into or withdrawn from a reactor core to manage neutron population and regulate the fission rate.

Neutron Moderator

A material surrounding fissile fuel in a reactor core that decelerates fast fission neutrons through atomic collisions to thermal speeds, increasing their probability of capture by ${}^{235}\text{U}$ nuclei to sustain fission.

Uranium Enrichment

The technical process of increasing the concentration of fissile Uranium-235 (${}^{235}\text{U}$) relative to non-fissile Uranium-238 (${}^{238}\text{U}$) to ensure a controlled chain reaction can be maintained in nuclear fuel.

Primary and Secondary Coolant Systems

Dual fluid loops in a nuclear power station where primary coolant circulates through the core under high pressure to extract heat and transfers it across a heat exchanger to boil unpressurized secondary coolant into steam to spin a turbine-generator.

Nuclear Fusion

The nuclear reaction in which two light nuclei (such as deuterium ${}^2\text{H}$ and tritium ${}^3\text{H}$) combine under immense temperature and pressure to form a heavier nucleus (such as helium ${}^4\text{He}$), releasing energy and a free neutron.

Proton-Proton Cycle

The three-step nuclear fusion mechanism powering the Sun: ${}^1_1\text{p} + {}^1_1\text{p} \rightarrow {}^2_1\text{H} + {}^0_{+1}\text{e} + \nu$, followed by ${}^1_1\text{p} + {}^2_1\text{H} \rightarrow {}^3_2\text{He} + \gamma$, and concluding with ${}^3_2\text{He} + {}^3_2\text{He} \rightarrow {}^4_2\text{He} + {}^1_1\text{p} + {}^1_1\text{p}$.