Predicting Decay Modes

Therefore, 14SC undergoes radioactive decay by (3 emission, 

On the other hand, 14gO has 8 protons but only 6 neutrons. This imbalance of protons and neutrons can be corrected if a proton is transformed into a neutron as is summarized by the equation 

14sO undergoes decay by positron emission, 

Electron capture accomplishes the same end result as positron emission, but because the nuclear charge is low, positron emission is the expected decay mode in this case. Generally, electron capture is not a competing process unless Z 30 or so. 

Although the use of the number of protons and neutrons to predict stability is straightforward, there are further applications of the principles discussed that are useful also. For example, consider the following cases  

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FIGURE 1.14 Predicting decay mode from the relative number of protons and neutrons. 

Predict the decay mode for the following and write the reaction for the predicted decay mode (a) 3516S (b) 179F (c) 4320Ca. 

Sometimes it is difficult to predict if a particular isotope is stable and, if unstable, what type of decay mode it might undergo. All isotopes that contain 84 or more protons are unstable. These unstable isotopes will undergo nuclear decay. For these large massive isotopes, we observe alpha decay most commonly. Alpha decay gets rid of four units of mass and two units of charge, thus helping to relieve the repulsive stress found in the nucleus of these isotopes. For other isotopes of atomic number less than 83, we can best predict stability by the use of the neutron to proton (n/p) ratio. 

A plot of the neutrons (n) versus the protons (p) for the known stable isotopes gives the nuclear belt of stability. (See your textbook for a figure of the belt of stability.) At the low end of this belt of stability (Z < 20), the n/p ratio is 1. At the high end (Z 80), the n/p ratio is about 1.5. We can then use the n/p ratio of the isotope to predict if it will be stable. If it is unstable, then the isotope will utilize a decay mode that will bring it back onto the belt of stability. 

Predict the mode of decay of the following nuclei 14C, 3H, nC, 233U, 138La. 

A continuing effort among experimentalists who study nuclei far from beta stability is the measurement of the atomic mass surface As a manifestation of the nuclear force and the nuclear many body system, atomic masses signal important features of nuclear structure on both a macroscopic and microscopic scale It has thus been a challenge to nuclear theorists to devise models which can reproduce the measured mass surface and to predict successfully the masses of new isotopes Both the measured mass surface and that beyond it which can be predicted by these models serve as important input to a variety of fundamental and applied problems, e g, nucleosynthesis calculations, predictions of decay modes of exotic nuclei far from stability, nuclear de-excitation by particle evaporation, decay heat simulations, etc ... 

Finally the high Ps rate could be used to improve on the search for rare or forbidden decays of ground state Ps. Table II summarizes the present values of such decay modes and theoretical predictions. 

The dependence of kp on the type of a-hydrogen is not known, nor can variations in ke be predicted easily. Mataga has studied amine quenching of triplet benzophenone by flash spectroscopy. N,N-dialkylanilines are the only amines which actually yield radical ions, and then only in polar solvents 157). He suggests two competing decay modes of the exciplex. Monoalkylanilines and tertiary aliphatic amines in any solvent and dialkylanilines in nonpolar solvents yield only radicals, presumably from the exciplex. Even though the oxidation potentials of tertiary aliphatic amines are so low that they quench triplet ketones at rates... 

The only stable isotope of fluorine is fluorine-19. Predict possible modes of decay for fluorine-21, fluorine-18, and fluorine-17. 

Predicting the Mode of Decay An unstable nuclide generally decays in a mode that shifts its N/Z ratio toward the band of stability. This fact is illustrated in Figure 23.2B, which expands a small region of Figure 23.2A to show all of the stable and many of the radioactive nuclides in that region, as well as their modes of decay. Note the following points, and then we ll apply them in a sample problem ... 

SAMPLE PROBLEM 23.3 Predicting the Mode of Nuclear Decay... 

Plan We use the N/Z ratio to decide where the nuclide lies relative to the band of stability and how its ratio compares with others in the nearby region of the band. Then, we predict which of the decay modes just discussed will yield a product nuclide that is closer to the band. 

Analyze We are asked to predict the modes of decay of two nuclei. 

SECTION 21.2 The neutron-to-proton ratio is an important factor determining nuclear stability. By comparing a nuclide s neutron-to-proton ratio with those in the band of stability, we can predict the mode of radioactive decay. In general, neutron-rich nuclei tend to emit beta particles proton-rich nuclei tend to either emit positrons or im-dergo electron capture and heavy nuclei tend to emit alpha particles. The presence of magic numbers of nucleons and an even number of protons and neutrons also help determine the stability of a nucleus. A nuclide may undergo a series of decay steps before a stable nuclide forms. This series of steps is called a radioactive series or a nuciear disintegration series. 

New forms of radioactivity were reported. Proton emission from ground states, predicted as the simplest decay mode of proton-rich nuclei and long searched for, was observed in 1982 for Lu (81 ms) produced by a heavy-ion reaction (Hofinann et al. 1982). Unusual large nuclear radii were found for some very light nuclei (Tanihata et al. 1985) and later attributed to neutron haloes, e.g., for Li (8.5 ms) to a halo of two neutrons around a i core. Even a new kind of natural radioactivity was discovered in 1984 (Rose and Jones 1984) emission of nuclei fi-om Ra (lid) leading to Discoveries of other rare decay modes involving the emission of a variety of fragments from very heavy nuclei soon followed. 

Analyze and Plan We are asked to predict the modes of decay of two nuclei. To do this we must calculate the neutron-to-proton ratios and compare the values with those for nudei that lie within the belt of stability shown in Figure 21.2. 

Predict the mode of decay of (a) plutonium-239 (b) indium-120. Keep in mind that our guidelines don t always work. For example, thorium-233, Th, which we might expect to undeigo alpha decay, actually undeigoes beta decay. Furthermore, a few radioactive nudei actually lie within the belt of stability. Both e d and Nd, for example, are stable and lie in the belt of stability. Nd, however, which lies between them, is radioactive. 

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