Nucleus neutron-proton ratios

Nuclei that have a neutron-proton ratio which is so high that they lie outside the belt of stable nuclei often decay by emission of a negative electron (a beta particle) from the nucleus. This effectively changes a neutron to a proton within the nucleus. Two examples are... 

In the previous section we saw that the stability of a nucleus is affected by its neutron/proton ratio. Even among those nuclei that we consider stable, however, there is a variation in the forces which hold the nucleus together. In order to study this variation in nuclear binding energy, let us consider the process of building a nucleus from protons and neutrons. For an example, let us look at the hypothetical reaction... 

Ag (e) the helium nucleus with one less neutron than proton and (f) the nucleus of barium whose neutron-proton ratio is 1.25. 

Neutrons readily induce nuclear reactions, but they always produce nuclides on the high neutron-proton side of the belt of stability. Protons must be added to the nucleus to produce an unstable nuclide with a low neutron-proton ratio. Because protons have positive charges, this means that the bombarding particle must have a positive charge. Nuclear reactions with positively charged particles require projectile particles that possess enough kinetic energy to overcome the electrical repulsion between two positive particles. 

Note The nucleus of each element may have more than one neutron/proton ratio (different isotopes) in the table are presented the most abundant stable isotopes of some elements and the number before their symbols represents very approximately the mass of that isotope (mass number, A). 

The alpha particle is a helium nucleus produced from the radioactive decay of heavy metals and some nuclear reactions. Alpha decay often occurs among nuclei that have a favorable neutron/proton ratio, but contain too many nucleons for stability. The alpha particle is a massive particle consisting of an assembly of two protons and two neutrons and a resultant charge of +2. 

A radioactive nucleus He transmutes into one of its isotopes through a neutron emission. What is the neutron/proton ratio in the new nucleus produced ... 

All elements with or more protons are unstable they eventually undergo decay. Other isotopes with fewer protons in their nucleus are also radioactive. The radioactivity corresponds to the neutron/proton ratio in the atom. If the neutron/proton ratio is too high (there are too many neutrons or too few protons), the isotope is said to be neutron rich and is, therefore, unstable. Likewise, if the neutron/proton ratio is too low (there are too few neutrons or too many protons), the isotope is unstable. The neutron/proton ratio for a certain element must fall within a certain range for the element to be stable. That s why some isotopes of an element are stable and others are radioactive. 

Notice that the mass number doesn t change in going from 1-131 to Xe-131, but the atomic number increases by one. In the iodine nucleus, a neutron was converted (decayed) into a proton and an electron, and the electron was emitted from the nucleus as a beta particle. Isotopes with a high neutron/ proton ratio often undergo beta emission, because this decay mode allows the number of neutrons to be decreased by one and the number of protons to be increased by one, thus lowering the neutron/proton ratio. 

Nuclides above the band of stabUity are unstable because their neutron/ proton ratio is too large. To decrease the number of neutrons, a neutron can be converted into a proton and an electron. The electron is emitted from the nucleus as a beta particle. A beta particle (j9) is an electron emitted from the nucleus during some kinds of radioactive decay. 

Another type of decay for nuclides that have a neutron/proton ratio that is too small is electron capture. In electron capture, an inner orbital electron is captured by the nucleus of its own atom. The inner orbital electron combines with a proton, and a neutron is formed. 

As noted already (see Fig. 1.6), the ratio of neutrons to protons in the nucleus of an element increases steadily as we move through the periodic table. The neutron/proton ratio for for example, is 1.55, while for a nucleus of around one half of the mass of the stable isotopes have neutron/proton ratios of around 1.30. The nuclei formed by fission are therefore neutron rich, with neutron/proton ratios which are appreciably higher than those characterizing the stable isotopes of the same species. The return of the fission product nuclei to the region of stable neutron/proton ratio may be accomplished, in the first place, by the emission of one or more neutrons and then, more slowly, by the mechanism of p emission (which is essentially the conversion of one of the neutrons in the nucleus to a proton). 

The capture of the neutron raises the neutron/proton ratio in the compound nucleus formed, favouring P emission. Reaction (18.5) is usually accompanied by y emission from the excited states of z+ Y. 

An alplia p uticle is an energetic helium nucleus. The alplia particle is released from a radioactive element witli a neutron to proton ratio tliat is too low. The helium nucleus consists of two protons and two neutrons. The alplia particle differs from a helimn atom in that it is emitted witliout any electrons. The resulting daughter product from tliis tj pe of transformation lias an atomic number Uiat is two less tluin its parent and an atomic mass number tliat is four less. Below is an e. aiiiple of alpha decay using polonium (Po) polonium has an atomic mass number of 210 (protons and neutrons) and atomic number of 84. 

Whether or not a given nucleus will be stable depends on its neutron-to-proton ratio. The 264 known stable nuclei, shown as red dots in Figure 2.5 (page 30), fall within a relatively... 

The magic numbers which impart stability to a nucleus are 2, 8, 20, 28, 50, 82 or 122. The isotope, 39K, has a magic number equal to its number of neutrons, so it is probably stable. The others have a larger neutron-to-proton ratio, making them neutron-rich nuclei, so 40K and 41K might be expected to decay by beta emission. In fact, both 39K and 41K are stable, and 40K does decay by beta emission. 

The stability of the atomic nucleus depends upon a critical balance between the repulsive and attractive forces involving the protons and neutrons. For the lighter elements, a neutron to proton ratio (N P) of about 1 1 is required for the nucleus to be stable but with increasing atomic mass, the N P ratio for a stable nucleus rises to a value of approximately 1.5 1. A nucleus whose N P ratio differs significantly from these values will undergo a nuclear reaction in order to restore the ratio and the element is said to be radioactive. There is, however, a maximum size above which any nucleus is unstable and most elements with atomic numbers greater than 82 are radioactive. 

Electron Capture Decay. Electron capture decay is a competing process to positron decay and thus results in an increase in the neutron-to-proton ratio in the nucleus. In this process, a bound, inner orbital electron is captured by the nucleus, resulting in the conversion of a proton into a neutron, the emission of a neutrino, and, if the daughter nucleus is left in an excited state, the emission of one or more gamma rays. The net reaction is shown below ... 

The main factor in determining whether a nucleus will decay is the neutron to proton ratio. Stable atoms have a neutron to proton ratio close to 1. The ratio in unstable atoms is greater than 1. Nature likes a balance between the neutrons and the protons, so the nuclei give off radioactivity in the form of alpha or beta particles in an attempt to bring the neutron to proton ratio closer to 1. 

Thorium-234 has 90 protons and 144 neutrons for a neutron to proton ratio greater than 1 (144 /90). Thorium-234 emits a beta particle. This particle is given off when a neutron breaks into a proton and an electron. The proton stays in the nucleus changing it to 91 protons which is Protactinium -234 while emitting the electron as a beta particle. 

Tritium is hydrogen of mass number 3, having two neutrons and a proton in its nucleus. It is radioactive (half-life 12.4 years) in common with many isotopes having a large neutron-to-proton ratio, tritium decays with emission of an electron (called a beta ray). Such a decay can be represented by the nuclear equation (see also Chap. 27) ... 

The neutron-to-proton ratio of an atom s nucleus determines its stability. Unstable nuclei undergo radioactive decay, emitting radiation in the process. 

It may surprise you to learn that of all the known isotopes, only about 17% are stable and don t decay spontaneously. In Chapter 4 you learned that the stability of an atom is determined by the neutron-to-proton ratio of its nucleus. You may be wondering if there is a way to know what type of radioactive decay a particular radioisotope will undergo. There is, and as you ll learn in this section, it is the neutron-to-proton ratio of the nucleus that determines the type of radioactive decay that will occur. 

To a certain degree, the stability of a nucleus can be correlated with its neu-tron-to-proton (n/p) ratio. For atoms with low atomic numbers (< 20), the most stable nuclei are those with neutron-to-proton ratios of 1 1. For example, helium ( He) has two neutrons and two protons, and a neutron-to-pro-ton ratio of 1 1. As atomic number increases, more and more neutrons are needed to produce a strong nuclear force that is sufficient to balance the electrostatic repulsion forces. Thus, the neutron-to-proton ratio for stable atoms gradually increases, reaching a maximum of approximately 1.5 1 for the largest atoms. An example of this is lead With 124 neutrons and 82... 

Beta decay A radioisotope that lies above the band of stability is unstable because it has too many neutrons relative to its number of protons. For example, unstable C has a neutron-to-proton ratio of 1.33 1, whereas stable elements of similar mass, such as and have neutron-to-proton ratios of approximately 1 1. It is not surprising then that undergoes beta decay, as this type of decay decreases the number of neutrons in the nucleus. 

Note that the atomic number of the product nucleus, has increased by one. The nitrogen-14 atom now has a stable neutron-to-proton ratio of 1 1. Thus, beta emission has the effect of increasing the stability of a neutron-rich atom by lowering its neutron-to-proton ratio. The resulting atom is closer to, if not within, the band of stability. 

Figure 25-9 shows the positron emission of a carbon-11 nucleus. Carbon-11 lies below the band of stability and has a low neutron-to-proton ratio of 0.8 1. Carbon-11 undergoes positron emission to form boron-11. Positron emission decreases the number of protons from six to five, and increases the number of neutrons from five to six. The resulting atom, has a neutron-to-proton ratio of 1.2 1, which is within the band of stability. 

The electron capture of rubidium-81 decreases the number of protons in the nucleus while the mass number remains the same. Thus, the neutron-to-proton ratio increases from 1.19 1 for... 

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