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. 

Nuclides that lie below the belt of stability have low neutron-proton ratios and must reduce their nuclear charges to become stable. These nuclides can convert protons into neutrons by positron emission. Positrons (symbolized jS ) are particles with the same mass as electrons but with a charge of -Ft instead of-1. Here are three examples ... 

A nuclide with a low neutron-proton ratio can also reduce its nuclear charge by capturing one of its 1 S orbital... 

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. 

C22-0034. Determine Z, A, and N for each of the following nuclides (a) the nuclide of neon that contains the same number of protons and neutrons (b) the nuclide of lead that contains 1.5 times as many neutrons as protons and (c) the nuclide of zirconium whose neutron-proton ratio is 1.25. 

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 nuclide with a neutron/proton ratio which is smaller than that for a stable isotope of the element can increase its ratio by undergoing ... 

We would expect a neutron proton ratio that is closer to 1 1 than that of 14 C. This would be achieved if the product were 14 N, which will be the result of /T decay ... 

Positron production occurs for nuclides that are below the zone of stability (those nuclides whose neutron/proton ratios are too small). The net effect of positron emission is to change a proton to a neutron. An example of positron emission would be... 

These reactions, which are extremely fast, are often balanced by the reverse reactions, so that an approximation known as nnclear statistical equilibrium can be applied. In this case, the most stable species, i.e. those possessing the highest binding energy, are favoured. The result depends on only three parameters, viz. temperature, density and neutron/proton ratio. The latter in its turn results from the previous nuclear reactions and the composition of the star at birth, through neon-22 (see above). 

If we remember that the neutron/proton ratio in heavy nuclei is about 1.5, then Zij1T1jt will be about 5(as/ac). Thus, the upper bound to the periodic table is given as a ratio of two constants relating to the strength of the nuclear and Coulomb forces. The ratio as/ac is about 20-25, and thus we expect about 100-125 chemical elements. 

One neglects the free decay of the neutron to the proton because the half-life for that decay (10.6 m) is too long to be relevant.] The neutron-proton ratio, n p, was determined by a Boltzmann factor, that is,... 

Another trend is that radioactive nuclei with higher neutron/proton ratios (top side of the band) tend to emit j8 particles, while nuclei with lower neutron/proton ratios (bottom side of the band) tend to undergo nuclear decay by positron emission, electron capture, or a emission. This makes sense if you think about it The nuclei on the top side of the band are neutron-rich and therefore undergo a process that decreases the neutron/proton ratio. The nuclei on the bottom side of the band, by contrast, are neutron-poor and therefore undergo processes that increase the neutron /proton ratio. (Take a minute to convince yourself that a emission does, in fact, increase the neutron/proton ratio for heavy nuclei in which n > p.)... 

This process decreases the neutron/proton ratio ... 

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 ... 

There are two additional modes of decay that are important. These, however, are exhibited only by man-made isotopes, in particular by those having low neutron/proton ratios (for example, eC10,8015, and i2Mg 3). The net effect of both types of decay is opposite to that in decay. A proton is converted to a neutron, the atomic number drops by a single unit, but there is no change in mass number. 

It is apparent from a glance at a list of the elements, together with their atomic weights and atomic numbers, that for the lighter elements (Z < 20), the neutron proton ratio lies close to unity (that is, the atomic weights are very nearly twice the atomic numbers). For stable isotopes cf elements of higher atomic numbers, the neutron proton ratio increases as illustrated in Table 27 2 until it exceeds 1.5 in the region of lead and... 

Since the neutron proton ratio for relatively stable nuclei having atomic numbers in the 90 s is greater than the ratio for those having atomic numbers in the 3G , 40 s, or 50 s, the fission of uranium yields products whicli would be too neutron rich for stability unless extra neutrons were emitted also. Some neutrons are indeed ejected (an average of about 2.5 neutrons per fission) thus, in a typical fission ... 

Even considering the extra neutrons that are given off, the fission fragments generally have neutron proton ratios higher than those for stable isotopes. Further adjustment of the neutron proton ratios occurs by emission of particles from the fission products. 

The known nuclides. The red dots indicate the nuclides that do not undergo radioactive decay. Note that as the number of protons (Z) in a nuclide increases, the neutron/proton ratio required for stability also increases. 

Light nuclides are stable when Z equals A — Z, that is, when the neutron/proton ratio is 1. However, for heavier elements the neutron/ proton ratio required for stability is greater than 1 and increases with Z. 

The /3 particle is assigned the mass number 0, since its mass is tiny compared with that of a proton or neutron. Because the value of Z is —1 for the /3 particle, the atomic number for the new nuclide is greater by 1 than for the original nuclide. Thus the net effect of f3-particle production is to change a neutron to a proton. We therefore expect nuclides that lie above the zone of stability (those nuclides whose neutron/proton ratios are too high) to be /3-particle producers. 

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