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Nuclear Chemistry - 3

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1  Modes of radioactive decay

 

 

Each is characterized by the manner in which a collated beam of the ray is deflected by a magnetic or electostatic field. By this means, the two of the three types of radiation were shown to consist of positive particles (alpha rays) and negative particles (beta rays) The neutral radiation was identified as a form of electromagnetic radiation that became known as gamma rays.

The differing charges and masses of the three kinds of radioactive decay are revealed when the radiation passes through an externally-applied electrostatic or magnetic field. Beta (β) particles, being extremely light electrons, are most strongly deflected toward the positive end of the field. Alpha (α) particles, being 2He2+ ions, are much more massive  than electrons, so their deflection is much smaller. Gamma (γ) rays, being electromagnetic radiation (uncharged photons) are not deflected at all.

electrostatic deflection of radiation

 

 

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Radioactive decay is a consequence of nuclear instability. This instability arises from the very strong electrostatic repulsion between the positively-charged protons crowded into the very small confines of the nucleus. Nuclear radii vary from about 1E-5 to 8E-5 Å, giving rise to proton-proton repulsive energies of the order of 108 kJ/mol. Although the nuclear binding force (the "strong force") is much more powerful, it falls off with distance much more rapidly. As the number of particles within the nucleus increases, the binding forces beween the more distant nucleons diminish much more rapidly than does the electrostatic repulsion; the latter therefore becomes more sigificant in heaver nuclei.

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2  Radioactive decay rates

A single unstable nucleus may decay almost as soon as it is formed, or it may last for millions of years before disintegrating. It is no more possible to predict when a particular nucleus will decay than to predict when an individual person will die. Radioactive decay, like mortality, is a stochastic process which must be treated statistically; using statistics and a sufficiently large sample, we can predict to any desired accuracy the fraction of atoms that will have decayed (or the fraction of a population that will no longer be alive) after a given time.

The activity of a sample of nuclei is the number of disintegrations per unit time. The activity is directly proportional to the number of undecayed nuclei present at any given time:

rate = –dN/dT = kN

In other words, the activity will fall off with time (hence the negative sign) at a decreasing rate (note the k[N] term; n, of course is continually decreasing as more nuclei decay.)

The activity is an example of a quantity whose rate of change depends on the instantaneous magnitude of that quantity. This very common functional relation is known as an exponential or first-order decay law; the rates of many chemical reactions follow such a law. The same law (but without the minus sign) describes the unrestricted growth of a population of bacteria, or of a compound-interest bank account.

The constant k in the equation is the decay constant; its value is a characteristic property of a given kind of nucleus. The more unstable the nucleus, the larger the value of k.

If the activity of a sample is A0 at time t=0 and A at time t, the ratio of these activities is given by the integrated form of Eq ?:

ln(A0/A) = ln N/N = -kt

After a certain time t1/2, half of the original sample of nuclei will have decayed. This time is known as the half-life

ln (1/2) = -kr = 0.693

The half-life is more commonly used than k to characterize the instability of nuclear species. The relation beetween these two quantities can be seen by rearranging the above equation:

r = 0.693/k

Problem example

The alpha-emitting americium isotope 95Am241 is used as an ion source in many kinds of residential smoke detectors. The half-life of this nuclide is 458 years. How long will it take for the activity to fall by five percent?

Solution

ln (A/A) = ln(0.95) = –kt = –0.693 (t/0.693 t /458 y

t = (458 y) (–0.051) / .693 = 34 y

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3  Natural radioisotopes and decay series

There are around 75 radioactive nuclides that occur naturally in the earth and its atmosphere. Many of these have such long half lifes that they are considered to have been present when the earth was formed. Among these are the most common isotopies of all the natural elements beyond 83Bi, as well as a number of other isotopes of lighter elements. Among this latter group is 19K40, which constitutes about 0.01% of natural potassium and is believed to be the major source of heat within the earth.

Any short-lived nuclides present when the earth was formed will of course have decayed a long time ago. This is the reason that the elements technetium (43Tc) and the halogen astatine (85At) are not found in nature.
Tc is the only element with an atomic number less than 83 that possesses no stable isotopes. As for At, its most stable (i.e., least unstable) isotope has a half life of only a few hours. The holes in the periodic table corresponding to these elements were not filled until the elements were prepared synthetically around 1940.

The natural radionuclides whose half lifes are much less than the age of the earth (about 4.5E9 y) must be presumed to be formed continuously from some other source. In most cases, the source is the decay of a longer-lived nuclide; if a long-lived nuclide decays into a short-lived species, the concentration of the latter will tend to be almost constant with time.

Most of the natural radioisotopes are the products of the decay of uranium (the heaviest naturelly-occurring element) or thorium. It was from pitchblende, an ore of uranium, that Marie and Pierre Curie first isolated other radioactive elements with half-lifes much shorter than that of uranium. This led to their discoveries of polonium (r=138 d), then radium (r = 1620 y) and also the noble gas radon (r = 3.8 d)

Three natural radioactive decay series have been identified. Each is known by the name of its parent nuclide: U238 (shown here), Th232, and U236. (A fourth series, based on Np237 with r=106 y has long since disappeared.) In each series, a sequence of alpha-decays eventually leads to a different stable isotope of lead. This is the cause of the considerable variation in the composition and average atomic weight of naturel lead ore deposits, and is the reason that the atomic weight of Pb cannot be speciied to more than four significant figures.

 

 

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