20.1 Nuclear Structure and Stability | Chemistry: Atoms First 2e

Learning Objectives

Describe nuclide notation, nucleon makeup, and nuclear versus chemical changes
Calculate mass defect, nuclear binding energy, and binding energy per nucleon
Explain nuclear stability trends, including the band of stability, magic numbers, and the binding energy curve

Core Concepts & Principles

Nuclear chemistry examines nuclear structure and changes. Nuclides are designated as ${}_{Z}^{A}\text{X}$ (mass number $A$ , atomic number $Z$ ). Protons and neutrons are nucleons. Unlike chemical reactions involving electron shells and small enthalpy changes, nuclear reactions alter nuclear structure and can release or absorb far more energy.

Nuclear Structure & Forces

Nuclei are extremely small ( $10^{-15}\text{ m}$ ) and dense ( $\sim 10^{14}\text{ g/cm}^3$ ). The short-range strong nuclear force overcomes electrostatic proton repulsions to bind nucleons together.

Mass Defect & Binding Energy

Mass defect ( $\Delta m$ ) is the mass difference between a nucleus and its separated constituent nucleons. Nuclear binding energy is the energy released during formation (or required for separation), calculated via the mass-energy equivalence equation ( $E = mc^2$ ). When using an atomic mass instead of a nuclear mass, include the masses of the atom's electrons in the separated-particle total. Mass must be converted from $\text{amu}$ to $\text{kg}$ ( $1\text{ amu} = 1.6605 \times 10^{-27}\text{ kg}$ ), and energy uses units such as joules, electron volts (eV), and $\text{MeV}$ .

Nuclear Stability & Trends

Stable nuclides form a narrow band of stability. Lighter nuclei have a $1:1$ neutron-to-proton ratio, while heavier nuclei require more neutrons to offset proton repulsion. Unstable radioisotopes exhibit radioactivity.

Even/Odd stability: Nuclei with even numbers of protons and/or neutrons are more likely to be stable.
Magic numbers: Specific proton or neutron counts ( $2, 8, 20, 28, 50, 82, 126$ ) form complete nuclear shells.
Binding energy per nucleon: Peaks near $A \approx 56$ (iron region). Suitable light nuclei can release energy through fusion, and suitable heavy nuclei through fission, when products have higher binding energy per nucleon.

Core Mental Model: Energy from Mass Defect

Mass-energy equivalence ( $E = mc^2$ ) shows that minuscule mass losses during nucleon binding release enormous energy compared to chemical bonding.

Problem-Solving Routines & Methods

Calculating Binding Energy per Nucleon

1
Calculate mass defect by subtracting observed atomic mass from the sum of constituent proton, neutron, and electron masses.
2
Convert mass defect from amu to kg using $1 \text{ amu} = 1.6605 \times 10^{-27} \text{ kg}$ .
3
Calculate total binding energy in Joules using $E = \Delta m c^2$ , then convert to MeV ( $1 \text{ MeV} = 1.602 \times 10^{-13} \text{ J}$ ).
4
Divide total binding energy by mass number $A$ to find binding energy per nucleon.

Pro-Tip: Ensure mass units match your speed of light units (\text{kg} with \text{m/s}) before applying

E = mc^2

Mass-Energy Equivalence

E = \Delta m c^2

Calculates energy equivalent of a mass defect.

Variables & Constants

E

=energy;

\Delta m

=mass defect;

c

=speed of light (

2.998 \times 10^8 \text{ m/s}

)

Binding Energy per Nucleon

\text{Binding energy per nucleon} = \frac{E_{\text{total}}}{A}

Determines stability per nucleon for a given nuclide.

Variables & Constants

E_{\text{total}}

=total nuclear binding energy;

A

=mass number

Practice & Concept Checks

Concept Check

Calculate the mass defect for a helium-4 atom (

{}_{2}^{4}\text{He}

) given an atomic mass of

4.0026 \text{ amu}

(proton =

1.0073 \text{ amu}

, neutron =

1.0087 \text{ amu}

, electron =

0.00055 \text{ amu}

Concept Check

Why do heavier stable nuclei require higher neutron-to-proton ratios than light stable nuclei?

Concept Check

Explain why the binding energy per nucleon curve peaks around iron (

A \approx 56

) and how this relates to nuclear fission and fusion.

Key Terms & Vocabulary

band of stabilityNuclear Structure and Stability

(also, belt of stability, zone of stability, or valley of stability) region of graph of number of protons versus number of neutrons containing stable (nonradioactive) nuclides

binding energy per nucleonNuclear Energy

total binding energy for the nucleus divided by the number of nucleons in the nucleus

electron volt (eV)Nuclear Energy

measurement unit of nuclear binding energies, with 1 eV equaling the amount energy due to the moving an electron across an electric potential difference of 1 volt

magic numberNuclear Structure and Stability

nuclei with specific numbers of nucleons that are within the band of stability

Example: A magic number is a proton or neutron count that fills a nuclear shell and increases stability; it does not guarantee that a nuclide is nonradioactive.

mass defectNuclear Energy

difference between the mass of an atom and the summed mass of its constituent subatomic particles (or the mass “lost” when nucleons are brought together to form a nucleus)

mass-energy equivalence equationNuclear Energy

Albert Einstein’s relationship showing that mass and energy are equivalent

nuclear binding energyNuclear Energy

energy lost when an atom’s nucleons are bound together (or the energy needed to break a nucleus into its constituent protons and neutrons)

nuclear chemistryNuclear Structure and Stability

study of the structure of atomic nuclei and processes that change nuclear structure

nucleonNuclear Structure and Stability

collective term for protons and neutrons in a nucleus

nuclideNuclear Structure and Stability

nucleus of a particular isotope

radioactivityNuclear Structure and Stability

phenomenon exhibited by an unstable nucleon that spontaneously undergoes change into a nucleon that is more stable; an unstable nucleon is said to be radioactive

Example: Source clarification: the changing object is a nuclide (a nucleus), rather than a single nucleon. The source glossary uses nucleon here.

radioisotopeNuclear Structure and Stability

isotope that is unstable and undergoes conversion into a different, more stable isotope

strong nuclear forceNuclear Structure and Stability

force of attraction between nucleons that holds a nucleus together