Nuclear Physics: Nuclei, Radioactivity, and Nuclear Energy

Comprehensive vocabulary flashcards covering atomic masses, nuclear structure, mass defect, binding energy, nuclear forces, radioactive decay laws, alpha/beta/gamma decay, nuclear fission reactors, and stellar fusion.

Atomic Mass Unit ($\text{u}$)

A standard unit of mass defined as $\frac{1}{12}\text{th}$ of the mass of an unbound carbon-12 ($^{12}\text{C}$) atom, equivalent to $1.660539 \times 10^{-27}\,\text{kg}$ or $931.6\,\text{MeV}$.

Isotopes

Atomic species of the same chemical element having identical atomic number ($Z$) and electronic structure, but differing mass numbers ($A$) and neutron numbers ($N$).

Neutron

A neutral subatomic nucleon discovered by James Chadwick in 1935 with a mass of $m_n = 1.00866\,\text{u} = 1.6749 \times 10^{-27}\,\text{kg}$, which is stable within the nucleus but unstable as a free particle with a mean life of about $1000\,\text{s}$.

Isobars

Nuclides of different chemical elements that share the same mass number ($A$) but have different atomic numbers ($Z$), such as $^3_1\text{H}$ and $^3_2\text{He}$.

Isotones

Nuclides that have the same neutron number ($N$) but different atomic numbers ($Z$), such as $^{198}_{80}\text{Hg}$ and $^{197}_{79}\text{Au}$.

Nuclear Radius

The radius of a nucleus with mass number $A$, governed by the relationship $R = R_0 A^{1/3}$, where $R_0 = 1.2 \times 10^{-15}\,\text{m}$.

Nuclear Density

The mass density of nuclear matter, which is independent of the mass number $A$ and is approximately constant across all nuclei at $2.3 \times 10^{17}\,\text{kg\,m}^{-3}$.

Mass Defect ($\Delta M$)

The difference between the total combined mass of the constituent protons and neutrons and the actual mass of the bound nucleus, given by $\Delta M = [Z m_p + (A - Z) m_n] - M$.

Nuclear Binding Energy ($E_b$)

The total energy released when constituent nucleons assemble into a bound nucleus, or equivalently, the total energy required to completely separate a nucleus into its individual constituent nucleons.

Binding Energy per Nucleon ($E_{bn}$)

The ratio of the total nuclear binding energy $E_b$ to the mass number $A$ ($E_{bn} = \frac{E_b}{A}$), serving as a direct measure of nuclear stability.

Binding Energy per Nucleon Curve

A plot of $E_{bn}$ versus mass number $A$, showing an approximately constant value of $8.5\,\text{MeV}$ for intermediate nuclei ($30 < A < 170$) with a maximum of about $8.75\,\text{MeV}$ for $^{56}\text{Fe}$, and declining values for both light ($A < 30$) and heavy ($A > 170$) nuclei.

Nuclear Force

A short-range, charge-independent attractive force acting equally between nucleons that is substantially stronger than the Coulomb force, falling rapidly to zero beyond a few femtometers and becoming repulsive at separations below approximately $0.8\,\text{fm}$.

$N/Z$ Ratio

The neutron-to-proton ratio required for nuclear stability ($1 \le \frac{N}{Z} \le 1.6$), which increases beyond unity in heavier nuclei to counteract electrostatic proton repulsion through additional attractive nuclear forces.

Radioactivity

A nuclear phenomenon wherein an unstable parent nucleus spontaneously disintegrates by emitting ionizing radiation such as alpha particles, beta particles, or gamma rays.

Law of Radioactive Decay

The physical principle stating that the disintegration rate per unit time is proportional to the total number of undecayed radioactive nuclei present in a sample: $\frac{dN}{dt} = -\lambda N$, leading to $N(t) = N_0 e^{-\lambda t}$.

Radioactive Decay Curve

An exponential decay plot showing the progressive reduction of undecayed nuclei $N$ over time according to $N = N_0 e^{-\lambda t}$, halving at each successive interval of half-life $T_{1/2}$.

Decay Constant ($\lambda$)

The characteristic proportionality constant or disintegration constant of a radionuclide that represents the decay probability per unit time.

Activity ($R$)

The total disintegration rate of a radioactive sample, defined mathematically as $R = -\frac{dN}{dt} = \lambda N = R_0 e^{-\lambda t}$.

Becquerel ($\text{Bq}$)

The SI unit of radioactive activity, defined as exactly $1$ disintegration or nuclear decay per second.

Curie ($\text{Ci}$)

A non-SI unit of radioactivity defined as $1\,\text{Ci} = 3.7 \times 10^{10}\,\text{decays per second} = 3.7 \times 10^{10}\,\text{Bq}$.

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

The duration of time required for the quantity of undecayed radioactive nuclei in a sample to decrease to half of its initial value, given by $T_{1/2} = \frac{\ln(2)}{\lambda} = \frac{0.693}{\lambda}$.

Mean Life ($\tau$)

The average lifetime of a radioactive nucleus before disintegrating, defined as $\tau = \frac{1}{\lambda}$ and related to half-life by $T_{1/2} = \tau \ln(2)$.

Alpha ($\alpha$) Decay

A mode of radioactive disintegration wherein an unstable nucleus $^A_Z\text{X}$ emits an alpha particle ($^4_2\text{He}$), yielding a daughter nucleus $^{A-4}_{Z-2}\text{Y}$ and positive disintegration energy $Q$.

Beta-Minus ($\beta^-$) Decay

A radioactive process wherein a neutron converts into a proton inside the nucleus, emitting an electron ($e^-$) and an antineutrino ($\bar{\nu}$): $n \rightarrow p + e^- + \bar{\nu}$.

Beta-Plus ($\beta^+$) Decay

A radioactive process occurring inside the nucleus where a proton converts into a neutron, emitting a positron ($e^+$) and a neutrino ($\nu$): $p \rightarrow n + e^+ + \nu$.

Gamma ($\gamma$) Decay of Cobalt-60 ($^{60}\text{Co}$)

A two-step nuclear de-excitation following $\beta^-$ decay of $^{60}_{27}\text{Co}$, where the excited $^{60}_{28}\text{Ni}$ daughter nucleus cascades down to its ground state by sequentially emitting two gamma photons of energies $E_\gamma = 1.17\,\text{MeV}$ and $E_\gamma = 1.33\,\text{MeV}$.

K-Capture

A nuclear transformation in which a nucleus captures an inner atomic electron (from the K-shell), converting a proton into a neutron with the emission of a neutrino: $^A_Z\text{X} + e^- \rightarrow ^A_{Z-1}\text{Y} + \nu$.

Nuclear Fission

A nuclear reaction wherein a heavy nucleus (such as $^{235}_{92}\text{U}$) absorbs a neutron and splits into two intermediate-mass fragments, producing free neutrons and releasing approximately $200\,\text{MeV}$ of energy.

Moderator

A light-nuclei medium within a nuclear reactor core (such as light water, heavy water $\text{D}_2\text{O}$, or graphite) used to slow fast fission neutrons down to thermal energies via elastic scattering.

Multiplication Factor ($K$)

The ratio of the number of fissions produced by a given generation of neutrons to the number of fissions produced in the preceding generation within a nuclear reactor.

Control Rods

Rods fabricated from neutron-absorbing materials such as cadmium that are inserted or withdrawn from the reactor core to adjust the multiplication factor $K$ and control the fission rate.

Nuclear Reactor

A thermal device engineered to initiate and control a self-sustaining nuclear fission chain reaction, consisting of a fuel core, moderator, control rods, reflector, coolant, and steam generator.

Thermonuclear Fusion

A nuclear reaction in which two light nuclei combine to form a heavier nucleus at extremely high temperatures (around $10^9\,\text{K}$), providing sufficient thermal kinetic energy to overcome electrostatic Coulomb repulsion.

Proton-Proton ($p\text{--}p$) Cycle

The multi-step thermonuclear fusion mechanism in the Sun's core where four hydrogen nuclei ($^1_1\text{H}$) combine to form a helium-4 ($^4_2\text{He}$) nucleus, releasing $26.7\,\text{MeV}$ of energy.