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Topic | Discussion | Learning Aids
Nucleons Atomic number | 31.1 NUCLEAR STRUCTURE The nucleus of an atom consists of protons and neutrons, which are collectively referred to as nucleons. A neutron is an elecrically neutral particle whose mass is slightly larger than that of the proton. The atomic number Z is the number of protons in the nucleus. The atomic mass number A (or nucleon number) is the total number of protons and neutrons in the nucleus: |
Atomic mass number (or nucleon number) |

| (31.1)

| where N is the number of neutrons. For an element whose chemical symbol is X, the symbol for the nucleus is . |
Isotopes | Nuclei that contain the same number of protons, but a different number of neutrons, are called isotopes. The approximate radius (in meters) of a nucleus is given by |
Radius of a nucleus |

| (31.2)

Strong nuclear force | 31.2 THE STRONG NUCLEAR FORCE AND THE STABILITY OF THE NUCLEUS The strong nuclear force is the force of attraction between nucleons (protons and neutrons) and is one of the three fundamental forces of nature. This force balances the electrostatic force of repulsion between protons and holds the nucleus together. The strong nuclear force has a very short range of action and is almost independent of electric charge.
31.3 THE MASS DEFECT OF THE NUCLEUS AND NUCLEAR BINDING ENERGY The binding energy of a nucleus is the energy required to separate the nucleus into its constituent protons and neutrons. The binding energy is equal to
Binding energy |

| (31.3)

Mass defect | where is the mass defect of the nucleus and c is the speed of light in a vacuum. The mass defect is the amount by which the sum of the individual masses of the protons and neutrons exceeds the mass of the intact nucleus. |
Atomic mass unit | When specifying nuclear masses, it is customary to use the atomic mass unit (u). One atomic mass unit has a mass of and is equivalent to an energy of 931.5 MeV. |
Radioactivity | 31.4 RADIOACTIVITY Unstable nuclei spontaneously decay by breaking apart or rearranging their internal structure in a process called radioactivity. Naturally occurring radioactivity produces , , and rays. rays consist of positively charged particles, each particle being the nucleus of helium. The general form for decay is |
Decay |

| The most common kind of ray consists of negatively charged particles, or particles, which are electrons. The general form for decay is |
Decay |

Positron | decay produces another kind of ray, which consists of positively charged particles, or particles. A particle, also called a positron, has the same mass as an electron, but carries a charge of instead of. |
Transmutation | If a radioactive parent nucleus disintegrates into a daughter nucleus that has a different atomic number, such as that which occurs in and decay, one element has been converted into another element, the conversion being referred to as a transmutation. |
| rays are high-energy photons emitted by a radioactive nucleus. The general form for decay is |
Decay |

| decay does not cause a transmutation of one element into another. |
Neutrino | 31.5 THE NEUTRINO The neutrino is an electrically neutral particle that is emitted along with particles and has a mass that is much, much smaller than the mass of an electron.

Use Self-Assessment Test 31.1 to evaluate your understanding of Sections 31.1, 31.2, 31.3, 31.4 and 31.5 .

Half-life Activity | 31.6 RADIOACTIVE DECAY AND ACTIVITY The half-life of a radioactive isotope is the time required for one-half of the nuclei present to disintegrate or decay. The activity is the number of disintegrations per second that occur. Activity is the magnitude of , where is the change in the number N of radioactive nuclei and is the time interval during which the change occurs. In other words, activity is . The SI unit for activity is the becquerel (Bq), one becquerel being one disintegration per second. Activity is sometimes also measured in a unit called the curie (Ci); .
Radioactive decay obeys the following relation

| (31.4)

Decay constant | where is the decay constant. This equation can be solved by the methods of integral calculus to show that |
Number of nuclei remaining as a function of time |

| (31.5)

| where is the original number of nuclei. The decay constant is related to the half-life according to |
Decay constant and half-life |

| (31.6)

| 31.7 RADIOACTIVE DATING If an object contained radioactive nuclei when it was formed, then the decay of these nuclei can be used to determine the age of the object. One way to obtain the age is to relate the present activity A of an object to its initial activity : |
Activity as a function of time |

| where is the decay constant and t is the age of the object. For radiocarbon dating that uses the isotope of carbon, the initial activity is often assumed to be . 31.8 RADIOACTIVE DECAY SERIES The sequential decay of one nucleus after another is called a radioactive decay series. A decay series starts with a radioactive nucleus and ends with a completely stable nucleus. Figure 31-16 illustrates one such series that begins with uranium and ends with lead
31.9 RADIATION DETECTORS A number of devices are used to detect and particles, as well as rays. These include the Geiger counter, the scintillation counter, semiconductor detectors, cloud and bubble chambers, and photographic emulsions.

Use Self-Assessment Test 31.2 to evaluate your understanding of Sections 31.6, 31.7, 31.8 and 31.9 .

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