N/Z ratio

Eission products often are radioactive. This is because the fissioning nucleus has an // Z ratio of 1.54, so its products have a similar N Z ratio, hi contrast, stable nuclides in the = 77 to 157 range have ratios of around 1.3, so the products of fission have excess neutrons, making them unstable. 

The stability of nuclides is characterized by several important rules, two of which are briefly discussed here. The first is the so-called synunetry rule, which states that in a stable nuclide with low atomic number, the number of protons is approximately equal to the number of neutrons, or the neutron-to-proton ratio, N/Z, is approximately equal to unity. In stable nuclei with more than 20 protons or neutrons, the N/Z ratio is always greater than unity, with a maximum value of about 1.5 for the heaviest stable nuclei. The electrostatic Coulomb repulsion of the positively charged protons grows rapidly with increasing Z. To maintain the stability in the nuclei, more... 

The principal attraction in these studies is the ability to form reaction products or reaction intermediates with unusual N/Z ratios. By starting with nuclei that are either very proton rich or very neutron rich, new regions of nuclei can be reached and their properties studied. At higher energies, the unusual isospin of the intermediate species allows one to determine the effect of isospin on the properties of highly excited... 

For the mass 140 chain, Zp = 54.55 (Wahl, 1988). Note that this tabulated value of Zp/A (=54.55/140) is very close to that of the fissioning system, 92/236, that is, the N/Z ratio of the fragments is approximately that of the fissioning system. This idea is called the UCD (unchanged charge distribution) prescription. Therefore... 

Shortly after Chadwick s discovery, a group of physicists in Rome, led by Enrico Eermi, began to stndy the interaction of nentrons with the nnclei of various elements. The experiments prodnced a nnmber of radioactive species, and it was evident that the absorption of a nentron increased the N Z ratio in target nuclei above the stability line (see Fig. 19.1). One of the targets nsed was nranium, the heaviest naturally occurring element. Several radioactive prodncts resnlted, none of which had chemical properties characteristic of the elements between Z = 86 (radon) and Z = 92 (uranium). It appeared to the Italian scientists in 1934 that several new transuranic elements (Z > 92) had been synthesized, and an active period of investigation followed. 

Figure 26-1 A plot of the number of neutrons versus the number of protons in stable nuclei. As atomic number increases, the N/Z ratio (the decimal fractions) of the stable nuclei increases. The stable nuclei are located in an area known as the band of stability. Most radioactive nuclei occur outside this band. 

Nuclei differ in their stability, and some are so unstable that they undergo radioactive decay. The ratio of the number of neutrons to number of protons (N/Z) in a nucleus correlates with its stability. Calculate the N/Z ratio for (a) Sm (b) Fe (c) °Ne (d) ° Ag. (e) The radioactive isotope decays in a series of nuclear reactions that includes another uranium isotope, and three lead isotopes, Pb, °Pb, and ° Pb. How many neutrons, protons, and electrons are in each of these fi ve isotopes ... 

N) versus number of protons (Z) for all nuclei shows a narrow band of stable nuclei. To become more stable the type of decay can often be predicted from the N/Z ratio of the unstable nucleus. Certain heavy nuclei undergo a series of decays to reach stability. 

The Band of Stability and the Neutron-to-Proton (N/Z) Ratio A key factor that determines the stability of a nuclide is the ratio of the number of neutrons to the number of protons, the N/Z ratio, which we calculate from (A — Z)/Z. For lighter nuclides, one neutron for each proton N/Z 1) is enough to provide stability. However, for heavier nuclides to be stable, the number of neutrons must exceed the number of protons, and often by quite a lot. But, if the N/Z ratio is either too high or not high enough, the nuclide is unstable and decays. 

Figure 23.2A on the next page is a plot of number of neutrons vs. number of protons for the stable nuclides. The nuclides form a narrow band of stability that gradually increases from an N/Z ratio of 1, near Z = 10, to an IV/Z ratio slightly greater than 1.5, near Z = 83 for ° Bi. Several key points are as follows ... 

Figure 23.2 A plot of number of neutrons vs. number of protons for the stable nuclides. A, A plot of N vs. Z for all stable nuclides gives rise to a narrow band that veers above N/Z = 1 shortly beyond Z = 10. The N/Z values for several stable nuclides are given. The most common modes of decay for unstable nuclides in a particular region are shown nuclides with a high N/Z ratio often undergo p decay those with a low ratio undergo e capture or positron emission heavy nuclei beyond the stable band (and a few lighter ones) undergo ot decay. B, The blue box in part A is expanded to show the stable and many of the unstable nuclides in that area. Note the modes of decay a decay decreases both N and Z by 2 P decay decreases N and increases Z by 1 positron emission and e capture increase N and decrease Z by 1.

Plan In order to evaluate the stability of each nuclide, we determine the NjZ ratio from (A — Z)/Z, the value of Z, stable N/Z ratios (from Figure 23.2), and whether Z and N are even or odd. 

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 ... 

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. 

Solution (a) This nuclide has an N/Z ratio of 1.4, which is too high for this region of the band. It will probably undergo p decay, increasing Z to 6 and lowering the N/Z ratio to 1. 

N/Z ratio The ratio of the number of neutrons to the number of protons, a key factor that determines the stability of a nuclide. (767)... 

We can imderstand why the N Z ratio must increase with atomic number in order to have nuclear stability when we consider that the protons in the nucleus must experience a repulsive Coulomb force. The fact that stable nuclei exist means that there must be an attractive force tending to hold the neutrons and protons together. This attractive nuclear force must be sufficient in stable nuclei to overcome the disruptive Coulomb force. Conversely, in unstable nuclei there is a net imbalance between the attractive nuclear force and the disruptive Coulomb force. As the number of protons increases, the total r ulsive Coulomb force must increase. Therefore, to provide sufficient attractive force for stability the number of neutrons increases more rapidly than that of the protons. 

In order to make isotopes of new elements having high N/Z ratios, there has been more recent interest in hot fusion reactions involving nuclei such as and Es as targets and light ions... 

The nuclides in the natural radioactive decay chains are not the most favorable candidates for heavy ion emission they have unfavorable N/Z ratios. As shown in the example of emission of oxygen isotopes by Th, emission of a Z = JVfragment leads to a product that is far from the center of P stability. Of course, emitting a fragment with N> Z (e.g., °0) displaces the emitted... 

The great majority of nuclei are unstable and undergo various types of radioactive decay a decay, p decay, positron emission, electron capture, and -y emission. In nuclear reactions, total mass number (A) and total charge (Z) must be balanced. A plot of number of neutrons (N) versus number of protons (Z) for all nuclei shows a narrow band of stable nuclei. To become more stable the type of decay can often be predicted from the N/Z ratio of the unstable nucleus. Certain heavy nuclei undergo a series of decays to reach stabiity. 

The N/Z ratio of stable nuclides gradually increases as Z increases. No stable... 

---