Nuclei

The One Thing

Nuclear stability and energy release depend on how strongly nucleons are bound within the nucleus. Mass defect appears as binding energy according to $E=\Delta m{c}^2$, and energy is released when fission or fusion produces nuclei with greater binding energy per nucleon.

Reactions, Processes and Experiments

Key Terms

• Nucleus: The small, dense central part of an atom containing protons and neutrons.
• Nucleon: A particle present in the nucleus; protons and neutrons are both nucleons.
• Atomic number ($Z$): The number of protons in a nucleus; it identifies the element.
• Mass number ($A$): The total number of nucleons, given by $A=Z+N$, where $N$ is the number of neutrons.
• Isotopes: Atoms of the same element having the same atomic number but different mass numbers.
• Nuclear notation: The notation ${}_Z^{A}X$, where $X$ is the element symbol, $Z$ is the atomic number, and $A$ is the mass number.
• Number of neutrons: $N=A-Z$.
• Nuclear radius: The approximate radius of a nucleus, given by $R=R_0{A}^{1/3}$, where $R_0$ is about $1.2\mathrm{fm}$, or approximately $1.2\times 10^{-15}\mathrm{m}$.
• Nuclear density: The density of nuclear matter, which is approximately constant because nuclear volume is proportional to $A$.
• Nuclear force: A very strong, short-range attractive force between nucleons that holds the nucleus together.
• Mass defect: The difference between the total mass of separate nucleons and the actual mass of the bound nucleus.
• Binding energy: The energy required to completely separate a nucleus into its individual protons and neutrons; it is also the energy released when the nucleus forms.
• Binding energy per nucleon: The average binding energy of each nucleon, calculated as total binding energy divided by mass number; it indicates nuclear stability.
• Nuclear fission: The splitting of a heavy nucleus into two medium-sized nuclei, usually with the release of neutrons and energy.
• Nuclear fusion: The combination of two light nuclei to form a heavier nucleus, releasing energy when the final nucleus is more tightly bound.
• Chain reaction: A self-sustaining sequence in which neutrons from one fission event cause further fission events.
• Critical mass: The minimum amount of fissile material needed to maintain a self-sustaining nuclear chain reaction.
• Nuclear force range: Nuclear force is effective only over a short range of about 1 to 2 fm.
• Nuclear-force saturation: A nucleon interacts mainly with nearby nucleons rather than equally with every nucleon in the nucleus.
• Mass-energy relation: $E=\Delta m{c}^2$, expressing the conversion of mass defect into binding energy.
• Atomic-mass binding-energy conversion: If mass defect is expressed in atomic mass units, binding energy in MeV is approximately $\Delta m(u)\times 931.5\mathrm{MeV}$.
• Mass defect using atomic masses: $\Delta m=Z{m}_H+(A-Z)m_n-M_{\text{atom}}$, where $m_H$ is the mass of a hydrogen atom, $m_n$ is the neutron mass, and $M_{\text{atom}}$ is the mass of the neutral atom.

Easily Confused

• Atomic number $Z$ and mass number $A$: $Z$ counts protons and identifies the element, whereas $A$ counts all nucleons.
• Mass defect and binding energy: Mass defect is the missing mass of the bound nucleus; binding energy is the corresponding energy given by $E=\Delta m{c}^2$.
• Fission and fusion: Fission splits a heavy nucleus into lighter nuclei, whereas fusion combines light nuclei into a heavier nucleus.
• Alpha, beta-minus and beta-plus decay: Alpha decay emits a helium nucleus; beta-minus decay changes a neutron into a proton; beta-plus decay changes a proton into a neutron.
• Beta decay and gamma decay: Beta decay changes the atomic number, whereas gamma decay changes neither atomic number nor mass number.
• Binding energy and binding energy per nucleon: Binding energy is the total energy holding the nucleus together; binding energy per nucleon is the average value used to compare nuclear stability.
• Nuclear force and electrostatic force: Nuclear force is a short-range attractive force between nucleons, whereas electrostatic force between protons is repulsive.
• Fission chain reaction and critical mass: A chain reaction is the continuing sequence of fission events; critical mass is the minimum fissile-material quantity required to sustain it.
• Nuclear and chemical energy: Nuclear energy involves changes in nuclear binding energy, whereas chemical energy involves changes in electron arrangements.

What Gets Asked

• Nuclear notation and composition: Questions may require interpretation of ${}_Z^{A}X$, calculation of neutron number using $N=A-Z$, or identification of isotopes. The common mark-losing error is confusing $A$, the total number of nucleons, with $Z$, the number of protons.
• Nuclear size and density: Questions may use $R=R_0{A}^{1/3}$ or ask why nuclear density is nearly independent of mass number. The key point is that nuclear volume is proportional to $A$.
• Mass defect and binding energy: Questions may require use of $E=\Delta m{c}^2$, the atomic-mass expression $\Delta m=Z{m}_H+(A-Z)m_n-M_{\text{atom}}$, or the conversion $\Delta m(u)\times 931.5\mathrm{MeV}$. A frequent error is treating mass defect as energy without applying the appropriate conversion.
• Nuclear stability: Questions may ask why nuclei near iron and nickel are especially stable or require comparison using binding energy per nucleon. Greater binding energy per nucleon generally indicates greater stability.
• Radioactive decay: Questions may ask how alpha, beta-minus, beta-plus or gamma decay changes $A$ and $Z$. Gamma decay changes neither number, while beta decay changes $Z$ but not $A$.
• Fission and fusion: Questions may compare their mechanisms, conditions and energy release. Fission involves heavy nuclei and chain reactions; fusion involves light nuclei and requires extremely high temperature and pressure to overcome electrostatic repulsion.