University Physics Volume 3

# Summary

### 10.1Properties of Nuclei

• The atomic nucleus is composed of protons and neutrons.
• The number of protons in the nucleus is given by the atomic number, Z. The number of neutrons in the nucleus is the neutron number, N. The number of nucleons is mass number, A.
• Atomic nuclei with the same atomic number, Z, but different neutron numbers, N, are isotopes of the same element.
• The atomic mass of an element is the weighted average of the masses of its isotopes.

### 10.2Nuclear Binding Energy

• The mass defect of a nucleus is the difference between the total mass of a nucleus and the sum of the masses of all its constituent nucleons.
• The binding energy (BE) of a nucleus is equal to the amount of energy released in forming the nucleus, or the mass defect multiplied by the speed of light squared.
• A graph of binding energy per nucleon (BEN) versus atomic number A implies that nuclei divided or combined release an enormous amount of energy.
• The binding energy of a nucleon in a nucleus is analogous to the ionization energy of an electron in an atom.

• In the decay of a radioactive substance, if the decay constant ($λλ$) is large, the half-life is small, and vice versa.
• The radioactive decay law, $N=N0e−λt,N=N0e−λt,$ uses the properties of radioactive substances to estimate the age of a substance.
• Radioactive carbon has the same chemistry as stable carbon, so it mixes into the ecosphere and eventually becomes part of every living organism. By comparing the abundance of $14C14C$ in an artifact with the normal abundance in living tissue, it is possible to determine the artifact’s age.

### 10.4Nuclear Reactions

• The three types of nuclear radiation are alpha ($αα$) rays, beta ($ββ$) rays, and gamma ($γγ$) rays.
• We represent $αα$ decay symbolically by $ZAX→Z−2A−4X+24HeZAX→Z−2A−4X+24He$. There are two types of $ββ$ decay: either an electron ($β−β−$) or a positron ($β+β+$) is emitted by a nucleus. $γγ$ decay is represented symbolically by $ZAX*→ZAX+γZAX*→ZAX+γ$.
• When a heavy nucleus decays to a lighter one, the lighter daughter nucleus can become the parent nucleus for the next decay, and so on, producing a decay series.

### 10.5Fission

• Nuclear fission is a process in which the sum of the masses of the product nuclei are less than the masses of the reactants.
• Energy changes in a nuclear fission reaction can be understood in terms of the binding energy per nucleon curve.
• The production of new or different isotopes by nuclear transformation is called breeding, and reactors designed for this purpose are called breeder reactors.

### 10.6Nuclear Fusion

• Nuclear fusion is a reaction in which two nuclei are combined to form a larger nucleus; energy is released when light nuclei are fused to form medium-mass nuclei.
• The amount of energy released by a fusion reaction is known as the Q value.
• Nuclear fusion explains the reaction between deuterium and tritium that produces a fusion (or hydrogen) bomb; fusion also explains the production of energy in the Sun, the process of nucleosynthesis, and the creation of the heavy elements.

### 10.7Medical Applications and Biological Effects of Nuclear Radiation

• Nuclear technology is used in medicine to locate and study diseased tissue using special drugs called radiopharmaceuticals. Radioactive tags are used to identify cancer cells in the bones, brain tumors, and Alzheimer’s disease, and to monitor the function of body organs, such as blood flow, heart muscle activity, and iodine uptake in the thyroid gland.
• The biological effects of ionizing radiation are due to two effects it has on cells: interference with cell reproduction and destruction of cell function.
• Common sources of radiation include that emitted by Earth due to the isotopes of uranium, thorium, and potassium; natural radiation from cosmic rays, soils, and building materials, and artificial sources from medical and dental diagnostic tests.
• Biological effects of nuclear radiation are expressed by many different physical quantities and in many different units, including the rad or radiation dose unit.