Chapter 6
Nuclides composite particles of nucleons
Discovery consists in seeing what everyone else has seen and thinking what no one else has thought.
Albert Szent-Gyorgi
A nuclide is a type of atoms whose nuclei have specific numbers of protons and neutrons (nucleons). The standard model considers up and down quarks as basic components of nuclei, but nucleons (protons and neutrons) are convenient units. On the other hand, nuclides are energy states in the form of masses. Stable states remain unchanged for an indefinite period whereas unstable ones undergo radioactive decay. For example, the energy equivalents of protons, deuterons and 238U are 938 MeV, 1.88 GeV and 212 GeV respectively. For convenience, we discuss nuclides in terms of nucleons.
Discoveries of protons and neutrons infer the existence of isotopes. Since isotopes refer to atoms of the same element with different number of neutron, the term nuclide is more appropriate when referring to a type of atom. Nuclear properties are specific for nuclides, but not necessarily for chemical elements.
The number of protons is the same as the atomic number, Z, and the mass number, A, is the number of nucleons in the nucleus. Thus the number of neutrons, N, is A - Z. Any nuclide is an isotope of an element, and the symbol of the element is used to represent the nuclide, but the mass number is given as a pre-superscript, such as 16O, where 16 is the mass number. For clarity and convenience, the atomic number is given as a post-superscript, 16O8.
Stable nuclides exist for an indefinite period of time, and they are the constituents of ordinary material. Unstable nuclides emit subatomic particles, with 4, n, p being the most common. Few undergo nuclear fission. However, radioactive nuclides with long half-lives are also present in nature.
Stable Nuclides
Stable nuclides remain unchanged for an indefinite period, and they are not radioactive. Of the natural elements on Earth, only elements with atomic number less than 83 have stable isotopes, except technetium (Tc, Z = 43) and promethium (Pm, Z = 61). Only 81 elements have at least one stable isotope. However, there are 280 stable nuclides, and many elements have more than one stable isotope. The composition of isotopes in an element is an important piece of information in many technologies. Elements with more than 92 protons are all man-made, as are technetium (Tc) and promethium (Pm), because they have no stable isotopes. Elements with atomic number greater than 83 have no stable isotopes, but they are decay products from uranium and thorium, and they are constantly produce, but at the same time they decay and convert eventually to Bi or Pb.
There are many factors affecting the stability of nuclides. In this section, we describe some common factors of stable nuclides. We can only describe one at a time, but all factors concertedly affect the stability of nuclides.
Numbers of Protons and Neutrons
Protons are charged but neutrons are not. Although they may not exist as individual nucleons in the nucleus, their numbers are obvious properties. From accounting point of view, we consider them as individuals.
- How do numbers of protons and neutrons affect the stability?
What is the role of neutrons in the atomic nuclei?
What are the ratios of neutron numbers to proton numbers for stable nuclides?
Do the ratios vary systematically?
We have examined some light nuclides in an Chapter 5 when we introduced the Nuclide Chart as a means to organize nuclear information. For convenience, we divide the large Nuclide Chart into three sections: light-weight nuclides with atomic number less than 20 (Z 20), medium-weight nuclides with 20 < Z < 50, and heavy- weight nuclides with Z 50.
Light-weight nuclides are given in the next page. Some general observations regarding their stability are given below:
Only 1H and 3He have more protons than neutrons in their nuclei. Natural hydrogen contains 0.0015% of the isotope D, and only a trace of 3He is present in natural helium (mostly 4He). All other nuclides have either equal numbers of protons and neutrons or more neutrons than protons. The heaviest nuclide with equal numbers of protons and neutrons is 40Ca20, (20 being a magic number).
ZStable Nuclides
| (Magic numbers and double magic-number nuclides are in bold) (to be continued)
21 Sc
20 ...... Ca Ca Ca Ca Ca Ca
19 K K K
18 Ar Ar Ar .
17 Cl Cl
16 S S S S
15 ...... P
14 Si Si Si . .
13 Al
12 Mg Mg Mg . . .
11 Na
10 ...... Ne Ne Ne
9 F . . .
8 O O O
7 N N
6 C C . . . .
5 . . . . B B
4 Be . . . .
3 Li Li
2 He He . . . . .
1 P D N
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Most elements with odd atomic numbers, Z, have only one stable isotope. The number of stable isotopes generally increases as Z increases. Nuclides with odd numbers of neutrons have only one stable isotone (nuclides with the same number of neutrons), and the number of stable isotones also increases as the number of neutrons, N, increases.
Four nuclides 2D1, 6Li3, 10B5, and 14N7 have equal and odd numbers of protons and neutrons. For these light stable nuclides, the ratio N/Z ranges from 1 (D) to 1.22 (40Ar), ignoring H for which N/Z = 0. All but a few stable nuclides have more neutrons than protons. Uncharged neutrons probably moderate the proton-proton repulsion, making heavy nuclide stable.
A chart of stable nuclides with 20 < Z < 70 is given on the next page. For convenience in our discussion, nuclides with atomic numbers range between 20 (Ca) and 50 (Sn), two magic numbers called medium-weight nuclides.
A line with equal numbers of protons and neutrons is marked by “+” signs. For stable nuclides, the ratio N/I increases as Z (or N) increases: N/I = 1.14 for Sc (Z = 21), 1.27 for Nb (Z = 41), 1.41 for Sb (Z = 51), and 1.43 for Tb (Z = 65). The effect of this increase can be seen from the deviations of the locations of stable nuclides from the line marked by “+”.
Many stable isotopes appear on lines for Z = 8, 20, 28, 50, and 82 (see list below). Similarly, unusual numbers of stable isotones also appear on vertical lines with N = 8, 20, 28, 50, and 82. The existence of many stable nuclides with these numbers of protons or neutrons supports calling them magic numbers.
For the medium-weight nuclides, 1 (40Ca) < N/Z < 1.48 (124Sn50). However, 1 < N/Z < 1.40 for the six stable isotopes of calcium alone: 40Ca20, 42Ca20, 43Ca20, 44Ca20, 46Ca20, and 48Ca20. There are ten (10) stable isotopes of tin (112, 114, 115, 116, 117, 118, 119, 120, 122, & 124Sn50), for which 1.24 < N/Z < 1.48.
Because we run out of room in the graph above, the stable isotopes of elements with Z > 70 are listed below with their mass numbers. Number of neutrons (N) can be evaluated by subtracting the atomic number (Z) from the mass number (A), N = A - Z.
In the table below, the abundance in percentage, %, of the isotopes are given in the parentheses (% omitted). Gold (Au) and bismuth (Bi) are two elements that have only one stable isotope, the percentages of 197Au and 209Bi are 100%.
Mass Numbers of Heavy Stable Elements (70 < Z)
Z Symbol Mass (abundance or half life)
71Lu175 (97.4), 176 (2.6)
72Hf174 (0.163), 176 (5.21), 177 (18.56), 178 (27.1), 179 (13.75), 180 (35.22)
73Ta180 (0.0123), 181 (99.9877)
74W180 (0.135), 182 (26.4), 183 (14.4), 184 (30.6), 186 (28.4)
75Re185 (37.07), 187 (62.93)
76Os184 (0.018), 186 (1.59), 187 (1.64), 188 (13.3), 189 (16.1), 190 (26.4), 192 (41.0)
77Ir191 (38.5), 193 (61.5)
78Pt190 (0.0127), 192 (0.78), 194 (32.9), 195 (33.8), 196 (25.2), 198 (7.19)
79Au197 (100)
80Hg196 (0.146), 198 (10.02), 199 (16.84), 200(23.13), 201(13.22), 202(29.8), 204(6.85)
81Tl203 (29.5), 205 (70.5)
82Pb204 (1.4), 206 (25.1), 207 (21.7), 208 (52.3)
83Bi209 (100)
90Th232 (100% half life 1.4x1010 y)
92U235 (0.720, half life 7.04x108 y), 238 (99.276, half life 4.5x109 y)
For more information about nuclides, consult the Handbook of Chemistry and Physics by CRC Press, and the Handbook of Isotopes by CRC Press. More information about the Nuclide Chart is also available from the following web sites:
The contents in these web sites include the following.
- Description of the US Nuclear Data Network
- Center for Nuclear Information Technology, San Jose State University
- Idaho National Engineering Laboratory
- Isotopes Project, Ernest Orlando Lawrence Berkeley National Laboratory
- Lund Nuclear Data Service, University of Lund, Sweden
- Tandem Accelerator Laboratory, McMaster University, Canada
- National Nuclear Data Center, Brookhaven National Laboratory
- Nuclear Data Evaluation Project, Triangle Universities Nuclear Laboratory
- Nuclear Data Project, Oak Ridge National Laboratory
- Permanent Mass-chain Evaluation Responsibilities
- International Nuclear Structure and Decay Data Network (NSDD)
- Glossary of nuclear data evaluation and WWW jargon
Skill Building Questions
- How does the ratio N/Z vary as Z or N increases?
- What are the stable nuclides that have equal numbers of protons and neutrons. Which of these have odd atomic numbers?
- Which medium-weight elements do not have stable isotopes? What are their atomic numbers? How many stable isotones are there with N = 19, 31, 35, 39, 61, and 89?
- Can you calculate the atomic weight of say lead (Pb) from the abundance given to each stable isotope in the table of heavy stable nuclide, why or why not? If not, what more information is required?
Pairing of Nucleons
Since free nucleons have ½ spin, they obey Pauli's exclusion principle by allowing two protons or neutrons each with opposite spin to occupy a quantum state (if they are nucleons in a nucleus). There is a preference for having pairs of protons or neutrons, and it is known as pairing of nucleons.
- How does pairing of protons and neutrons affect the stability of nuclides?
What evidence suggests pairing of nucleons contributes to the stability of nuclide?
The numbers of stable nuclides due to even or odd numbers of protons and neutrons seem to suggest support the preference theory.
There are 166 stable nuclides with both Z and N even, 57 with even Z odd N, and 53 with odd Z even N. The only 4 light stable nuclides with both Z and N being odd are 2D1, 6Li3, 10B5, and 14N7. Note that H, Li, and B have two stable isotopes, which belong to the odd-even type. The distribution of stable nuclides due to odd and even number of Z and N can be interpreted as due to pairing of nucleons. We have mentioned that technetium (Z = 43) and promethium (Z = 61) have no stable isotopes. There are no stable isotones for N = 19, 31, 35, 39, 61, and 89.
The distinction between stable and long-lived nuclides is vague, but we choose to list the stable ones only. The effect of pairing also affects the abundance of the isotopes in elements, as well as the abundance of a nuclide on a planet, galactic or universal scale.
Pairing of nucleons also affects the decay or transmutation of unstable nuclides, particularly transmutation of isobars with even mass numbers A. For this type of nuclide, a beta decay converts an even-even nuclide into an odd-odd nuclide.
Skill Building Questions
- Which medium elements do not have stable isotopes?
What are their atomic numbers? How many stable isotones are there with N = 19, 31, 35, 39, 61, and 89?
- How many stable isotones are there with N = 2, 8, 20, 50, and 82?
Magic Numbers of Nucleons
Magic numbers 2, 8, 20, 28, 50, 82, and 126 have been mentioned in previous chapters in connection with the shell model of nuclear structures.
- How does the distribution of stable nuclides support a number to be a magic number?
How do magic numbers affect the stability of a nuclide?
One of the supports for the shell model comes from the fact that there are more stable isotopes with magic numbers of proton and more stable isotones with magic number of neutrons when compared to nuclides of similar mass numbers.
The emission of 4He2 (or particle) nuclei in the form of radioactive decay supports 2 as a magic number. Oxygen is a very abundant element, with 16O8 being the most abundant isotope (99.759%), plus 0.037% of 17O and 0.204% of 18O. There are 2 isotones (15N, 16O) with N = 8, plus the long-lived 14C. These data suggest 8 as a magic number.
There are 5 stable isotones with N = 20, but 0 with N=19, 1 with N = 21, and 3 each for N = 18 and 22. There are 6 stable Ca isotopes (Z = 20); the abundances of Ca isotopes are: 40Ca 96.97%, 42Ca 0.647%, 43Ca 0.145%, 44Ca 2.06%, 46Ca 0.0033%, 48Ca 0.185%. The light and heavy isotopes of Ca have 20 and 28 neutrons. There are also 5 Ni (Z = 28) isotopes and 4 isotones with 28 neutrons. These data reinforce the effect of pairing of protons, and pairing of neutrons and the magic numbers 20 and 28. Note that 4He2, 16O8, 40Ca20, 48Ca20, and 208Pb82 are double-magic-number nuclides, because they have magic number of protons and neutrons.
Numbers of stable isotopes and isotones for magic numbers 50 and 82 are very convincing. Furthermore, three families of radioactive series decay to a stable lead isotope (Z = 82) after many steps of transmutations.
The heaviest stable nuclide 209Bi83 has 126 neutrons; so has its isotone 208Pb82. You may think that two stable isotones are not impressive, but no heavier nuclides are stable.
So far, elements with Z = 112 have been artificially made. One of the objectives for people who synthesize heavy nuclides is to test the large magic numbers. Glenn T. Seaborg, a Nobel laureate in Chemistry (1951) believed that element 126 may have a half-life long enough to be observed. However, this element has not been observed yet.
Skill Building Questions
- What are magic numbers?
What are the reasons for them to be magic numbers?
- Give five double-magic number nuclides.
Abundances of Elements
The abundance of an element or nuclide is its amount in a system.
- What is the most abundant element in the universe?
How about the solar system and on the planet Earth?
How are they estimated and based on what evidences? - Is the abundance of a nuclide related to its stability?
Aside from stability, what else affects the abundance?
The sun has 99.9% of the mass of the solar system. Hydrogen atoms contribute 72%, and helium 4He 26% to all atoms in the Sun according to reliable estimates from spectroscopic, density, and meteorite studies. Light nuclides H and He are the major components of the Sun, where nuclear reactions convert H into He. Since stars are by far more massive than planets, the most abundant element in the universe is also hydrogen, followed by helium.
Taking as a whole, the most abundant element of the planet Earth is iron, which is the major component of the earth (molten) core. Additional evidence comes from the many iron meteorites, which are considered debris from outer space. However, the most abundant element of the Earth crust is oxygen in terms of number of atoms, but silicon is the most abundant element by mass. Their physical and chemical properties made them accumulate in different systems.
The atomic abundance (abundance based on the number of atoms) of elements are made from mineral and meteorites analyses. For example, the Earth crust is mostly silicate, SiO2, and the most abundant elements in the crust are O8 and Si14. Taking other data into consideration, oxygen is the most abundant element of the inner solar system, of which the Earth is a major part. The abundance of oxygen is given as 1 (log 1 = 0) for reference. Magnesium, silicon, and iron are the next most abundant elements, but their abundances are less than 0.5. Abundances of Ni, Ca, S, Al and Na are less than 0.1 whereas those of N and F are 0.0001 as shown in the diagram below.
The abundance of elements is one of the most important parameter in order to understand a planet, a satellite, or any body in the universe. Thus, space explorations include the probe to find the abundances of elements in the moon and mars.
The abundances of elements with even atomic numbers are usually higher than those with odd atomic numbers of comparable masses. The relative high abundances of O, Ca, Fe, Sn and Pb are due to the magic numbers 8, 20, 28, 50, and 82. Many factors influence the stability of nuclides and their abundances.
A general notion is that stable nuclides are abundant on a planetary or galactic scale. However, other factors such as the process of their synthesis and sources of nuclides for their productions also affect their abundances. The history and formation of the Sun, the Earth, and its satellite are different, and these differences give rise to their composition differences. The abundance, however, is partially related to their stability.
The group of elements C6, N7, O8, Ne10, Mg12, Si14, S16, Ar18, and Ca20 with even atomic numbers are relatively more abundant than the group with odd atomic numbers: F9, Na11, Al13, P15, and Cl17. The abundances of Li3, Be4, and B5 are very low. The abundance decreases from Ca20 on as the atomic numbers increase, but there is a relatively high peak at iron, Fe26, and nickel Ni28. Thus, the abundance strongly supports the theory that pairing of nucleons is an important factor for their stability.
Skill Building Questions
- What are the most abundant elements in the Earth crust and why?
- How do the magic numbers affect the abundances of elements or nuclides?
Mass and Stability of Nuclides
Unstable nuclides under go radioactive decay or fission, and they are radioactive nuclides. Some long-life unstable nuclides occur naturally, but many of them have been made artificially, and their properties well studied. Their making (synthesizing) involves nuclear reactions, which will be discussed in the next Chapter. We are only concerned with mass or energy regarding their stability in this section.
Aside from the stable isotopes of 12C and 13C, radioactive carbon isotopes with mass number 9, 10, 11, 14, 15 and 16 have been made and identified. Their half-lives are 127ms, 19.3 s, 20.3 m, 5730 y, 2.45 s, and 0.75 s respectively. Light carbon isotopes 9C, 10C, and 11C decay by emitting positrons or electron captures whereas heavy carbon isotopes 14C, 15C and 16C are beta emitters. Their masses hold the key for their stability. Radioactivity is a process by which unstable nuclides convert to stable ones.
The Binding Energy
Radioactivity or nuclear decays are spontaneous and exothermic reactions. The decay energy is the difference in total energy content before and after the decay. Energy and mass are equivalent, and the relative mass is the key to stability.
- Is the mass of a nuclide the sum of masses of its components?
Why or why not?
How is the mass of a nuclide related to its stability?
Masses of nuclides have been carefully measured, and the mass of a nuclide is usually less than the sum of masses of components. This suggests that the formation of a nuclide from its component is an exothermic reaction. For convenience in our discussion, a special name is given to the energy released when a nuclide is made from its components.