Chapter 29: Nuclear Physics

Nucleus

The central part of an atom, containing protons and neutrons.

Atomic Number (Z)

The number of protons in the nucleus of an atom; identifies the element.

Mass Number (A)

The sum of the number of protons and the number of neutrons in an atom.

Isotope

One of two or more atoms of the same element having different mass numbers due to differing numbers of neutrons.

Unified Atomic Mass Unit (u)

A unit used to describe the mass of a nucleus; 1 u = 1.6605 × 10^-27 kg.

Binding Energy

The difference between the sum of the mechanical energies of unbound nucleons and the mechanical energy of the assembled nucleus in its ground state.

Mass Defect

The difference between the mass of a nucleus and the sum of the masses of the individual nucleons that compose the nucleus; E_binding = Δmc².

Description of the Nucleus

• The diameter of the nucleus is about one ten-thousandth of an atom.
• Protons and neutrons are called nucleons.
• Over 99% of the mass of an atom is found in its nucleus.

Isotopes

• Atoms of the same element do not have the same number of neutrons.
• The term nuclide is often used interchangeably with isotope.
• Isotope notation shows the mass number (A) and the atomic number (Z).

Nuclear Stability

• Nuclei are often unstable.
• Physicists have postulated the existence of a strong nuclear force that binds protons and neutrons together.
• This force has a very small range of about 10^-15 m.
• Nuclei are stable if the ratio of their neutrons to protons is correct.
• For lighter, stable nuclei, the neutron to proton ratio is about 1:1.
• For larger nuclei, the ratio approaches 1.5:1.
• For nuclei with more than 82 protons, no number of neutrons provides stability.

Nuclear Shell Model

• The model currently used for the arrangement of nucleons in the nucleus that explains the stability of nuclei.
• The number of nucleons for a full shell is called the magic number for that shell.
• For protons, the magic numbers are 2, 8, 20, 28, 50, and 82.
• For neutrons, the magic numbers are 2, 8, 20, 28, 50, 82, and 126.
• When the numbers of protons and neutrons are both magic numbers, the nucleus is very stable.

Energy within the Nucleus

• Chemical energy is exchanged as bonds are broken and reformed.
• As a hypothetical nucleus is assembled from protons and neutrons, the decreases in potential energy will be released as other forms of energy.
• Nuclear stability is a function of the amount of nuclear binding energy per nucleon.
• Nuclei with mass numbers around A = 60 have the highest binding energy per nucleon and are thus the most stable.

Questions for Students

1. Describe the structure of the nucleus and the significance of the atomic number (Z) and mass number (A).
2. What is an isotope and how is it different from a nuclide?
3. Explain the concept of nuclear stability and the role of the strong nuclear force.
4. What are magic numbers in the context of the nuclear shell model?
5. How does binding energy relate to nuclear stability?