The structure of nuclei

Nuclei are composed of just two types of particles: protons and neutrons. These particles are referred to collectively as nucleons.

• The atomic number, Z, is equal to the number of protons in a nucleus. The neutron number, N, is the number of neutrons in a nucleus. The mass number of a nucleus, A, is the total number of nucleons it contains. Thus A = N + Z.

• A nucleus with atomic number Z and mass number A is designated as follows:

XAZ

The structure of nuclei

Isotopes are nuclei with the same atomic number but different neutron number.

• The atomic mass unit, u, which is defined so that the mass of is exactly 12u. The value of u is as follows:

• Neutrons and protons have masses slightly greater than 1u.

• The atomic mass unit can be expressed in terms of energy (MeV) as follows: 1u = 931.5 MeV/c2.

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The structure of nuclei

• The approximate radius of a nucleus of mass number A is given by

All nuclei have roughly the same density, regardless of their mass number.

• Nuclei are held together by the strong nuclear force. This force is attractive between all nucleons and has a range of only a few fermis.

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Radioactivity Radioactivity refers to the emissions observed when unstable nucleus change its

composition or when an exited nucleus decays to a lower-energy state.

1. Alpha decay: an particle ( the nucleus of helium atom) consist of two protons and two neutrons. A nucleus that emits an particle decreases its mass number by 4 and its atomic number by 2:

Where X is the parent nucleus and Y is the daughter nucleus.2. Beta decay refer to the emission of an electron, as when a neutron decays into a

proton, an electron, and an antineutrino:

This type of decay, which increases the atomic number by 1 but leaves the mass number unchanged, is referred to as decay. If a positron and neutrino are given off instead, we refer to the process as decay.

3. Gama decay occurs when an excited nucleus drops to a lower-energy state and emits a photon. In this case, neither the mass number nor atomic number is changed.

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Radioactivity

The activity of radioactive sample is equal to the number of decay per second. The units of activity are the curie (Ci) and the Becquerel (Bq)

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Half-life and radioactive dating

Radioactive nuclei decay with time in a well-defined way. As a result, many radioactive nuclei can be used as a type of “nuclear clock”

If the number of radioactive nuclei in a sample at time t = 0 is N0, the number, N, at a later time is

The constant , in this expression is referred to as the decay constant.

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Half-life and radioactive dating

The half-life of a radioactive material is the time required for half of its nuclei to decay. In terms of the decay constant, the half-life is

The rate at which radioactive nuclei decay is proportional to the number of nuclei present at any given time, and the decay constant:

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Half-life and radioactive dating

Carbon-14 can be used to date organic materials with ages up to about 15,000y. The age can be found using

Where Ro= 0.231 Bq is the initial activity, R is the present activity, and = 1.21 x 10-4y-1

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Practical applications of nuclear physics

Nuclear radiation can have both harmful and useful effects. An important way to characterize exposure to radiation is in terms of dosage, which can be defined in a number of ways.

Units of radiation

1. Roentgen, R is related to the amount of ionization charge produced by 200-keV x-ray in 1 kg of dry air at STP:

2. Rad (radiation absorbed dose) is a measure of the amount of energy absorbed by an irradiated material, regardless of the type of radiation:

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Units of radiation

3. RBE (relative biological effectiveness) takes into account that different types of radiation produce different amounts of biological damage

4. Combining the rad and the RBE yields the rem:

A dose of 1 rem of any type of radiation causes the same amount of biological damage.

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