Radioactive Decay

The time required for half of the atoms in any given quantity of a radioactive isotope to decay is the half-life of that isotope. Each particular isotope has its own half-life. For example, the half-life of 238U is 4.5 billion years. That is, in 4.5 billion years, half of the 238U on Earth will have decayed into other elements. In another 4.5 billion years, half of the remaining 238U will have decayed. One fourth of the original material will remain on Earth after 9 billion years. The half-life of 14C is 5730 years, thus it is useful for dating archaeological material. Nuclear half-lives range from tiny fractions of a second to many, many times the age of the universe. The formula used to calculate and elements half-life is:

The above formula is used in calculations involving the exponential
deacy of radioactive materials. 

If you want to
practice using the half-life calculator, use the following data. The
half-life of Radium 226 is 1,620 years. If you started with 100 grams,
in 3,240 years, 25 grams would be left.

1 Structure of the Atom

An atom consists of an extremely small, positively charged nucleus surrounded by a cloud of negatively charged electrons. Although typically the nucleus is less than one ten-thousandth the size of the atom, the nucleus contains more than 99.9% of the mass of the atom! Nuclei consist of positively charged protons and electrically neutral neutrons held together by the so-called strong or nuclear force. This force is much stronger than the familiar electrostatic force that binds the electrons to the nucleus, but its range is limited to distances on the order of a few x1015 meters.

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The number of protons in the nucleus, Z, is called the atomic number. This determines what chemical element the atom is. The number of neutrons in the nucleus is denoted by N. The atomic mass of the nucleus, A, is equal to Z + N. A given element can have many different isotopes, which differ from one another by the number of neutrons contained in the nuclei. In a neutral atom, the number of electrons orbiting the nucleus equals the number of protons in the nucleus. Since the electric charges of the proton and the electron are +1 and-1 respectively (in units of the proton charge), the net charge of the atom is zero. At present, there are 112 known elements which range from the lightest, hydrogen, to the recently discovered and yet to-be-named element 112. All of the elements heavier than uranium are man made. Among the elements are approximately 270 stable isotopes, and more than 2000 unstable isotopes.

2 Radioactivity

In 1896, Henri Becquerel was working with compounds containing the element uranium. To his surprise, he found that photographic plates covered to keep out light became fogged, or partially exposed, when these uranium compounds were anywhere near the plates. This fogging suggested that some kind of ray had passed through the plate coverings. Several materials other than uranium were also found to emit these penetrating rays. Materials that emit this kind of radiation are said to be radioactive and to undergo radioactive decay.

In 1899, Ernest Rutherford discovered that uranium compounds produce three different kinds of radiation. He separated the radiations according to their penetrating abilities and named them α alpha, β beta, and γ gamma radiation, after the first three letters of the Greek alphabet. The a radiation can be stopped by a sheet of paper. Rutherford later showed that an alpha particle is the nucleus of a He atom, 4He. Beta particles were later identified as high speed electrons. Six millimeters of aluminum are needed to stop most b particles. Several millimeters of lead are needed to stop g rays , which proved to be high energy photons. Alpha particles and g rays are emitted with a specific energy that depends on the radioactive isotope. Beta particles, however, are emitted with a continuous range of energies from zero up to the maximum allowed for by the particular isotope.

3 α Decay

The emission of an alpha particle, or 4He nucleus, is a process called a decay. Since a particles contain protons and neutrons, they must come from the nucleus of an atom. The nucleus that results from a decay will have a mass and charge different from those of the original nucleus. A change in nuclear charge means that the element has been changed into a different element. Only through such radioactive decays or nuclear reactions can transmutation, the age-old dream of the alchemists, actually occur. The mass number, A, of an a particle is four, so the mass number, A, of the decaying nucleus is reduced by four. The atomic number, Z, of 4He is two, and therefore the atomic number of the nucleus, the number of protons, is reduced by two.

4 β Decay

Beta particles are negatively charged electrons emitted by the nucleus. Since the mass of an electron is a tiny fraction of an atomic mass unit, the mass of a nucleus that undergoes b decay is changed by only a tiny amount. The mass number is unchanged. The nucleus contains no electrons. Rather, b decay occurs when a neutron is changed into a proton within the nucleus. An unseen neutrino,, accompanies each b decay. The number of protons, and thus the atomic number, is increased by one. For example, the isotope 14C is unstable and emits a ? particle, becoming the stable isotope 14N:

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5 γ Decay

Gamma rays are a type of electromagnetic radiation that results from a redistribution of electric charge within a nucleus. A g ray is a high energy photon. The only thing which distinguishes a g ray from the visible photons emitted by a light bulb is its wavelength; the g ray's wavelength is much shorter. For complex nuclei there are many different possible ways in which the neutrons and protons can be arranged within the nucleus. Gamma rays can be emitted when a nucleus undergoes a transition from one such configuration to another. For example, this can occur when the shape of the nucleus undergoes a change. Neither the mass number nor the atomic number is changed when a nucleus emits a γ ray in the reaction

152D gamma* --> 152D γ + γ

File translated from T_EX by T_TH, version 3.70.
On 12 Dec 2005, 18:13.