•There are still avenues of exploration and with many discoveries, new possibilities arise.
•There is no one-fits-all-uses Periodic Table — there are different arrangements to better explain some aspect of element linkages.
•The Periodic Table is a human construct, as can be seen from the names mentioned herein. And in recent times, seven individuals, in particular, have contributed greatly to modern philosophies of the Periodic Table and of the elements therein: Stephen Hawkes, William Jensen, Michael Laing, Pekka Pyykkö, Guillermo Restrepo, R. T. Sanderson, and Eric Scerri. The Reader will see their names (and many others) sprinkled in the text and among the Chapter References.
This book is not a data-filled comprehensive (and boring) compilation. Instead, by looking at some patterns and trends from different perspectives, the Author hopes that the Reader will find this book stimulating and thought-provoking. Without doubt, there are additional interesting and/or curious linkages and patterns of which the Author is unaware. Any Reader spotting an overlooked similarity or pattern is asked to bring it to the attention of the Author at: [email protected].
In closing, my Grenfell colleague Chris Frazee, and my partner, Marelene Rayner-Canham, are thanked for reading the entire manuscript (Marelene, many times) in an endeavor to minimize the errors therein.
Geoff Rayner-Canham
Chapter 0
The Periodic Table Exploration Begins!
“The time has come,” the Walrus said,
To talk of many things:
Of shoes—and ships—and sealing wax—
Of cabbages—and kings—
And why the sea is boiling hot—
And whether pigs have wings.”
Thus spake the Walrus to the Carpenter (Figure 0.1) in Alice Through the Looking Glass [1].
Here, in this treatise, Gentle Reader, you will be led through the world of the Periodic Table; a world even more exciting, more wondrous, more bizarre, than anything Lewis Carroll could have ever imagined.
Figure 0.1 The Walrus, the Carpenter, and the Little Oysters.
Reference
1.L. Carroll, More Annotated Alice: Alice’s Adventures in Wonderland and Through the Looking Glass and What Alice Found There, with notes by Martin Gardner; Random House, New York, NY, 220 (1990).
Chapter 1
Isotopes and Nuclear Patterns
In the early decades of modern chemistry, atomic mass (weight) of an element was a major topic for debate and heated dispute. The original Periodic Tables were constructed in terms of order of atomic mass. Any irregularities in order were excused away. With the discovery of atomic number and its use as the foundation of the modern Periodic Table, inorganic chemists seem to have largely ignored patterns in element isotopes. Not only do such patterns explain average atomic mass irregularities, but they reveal some fascinating nuclear chemistry. In addition, the shell model of the nucleus is important in the synthesis of new chemical elements.
In this chapter, the principles of nuclear physics will only be developed to a depth that will aid the understanding of the properties of atoms. For example, the origins of the nuclear strong force, which holds nuclear particles together, is best explained in terms of constituent quarks [1], far beyond the realm of this book. Similarly, the nuclear shell model will be used and applied without delving deeply into its quantum mechanical basis.
Proton–Neutron Ratio
For the lower proton numbers, P, the number of neutrons, N, is approximately matching. With increasing numbers of protons, the numbers of neutrons necessary for nuclear stability increase at a faster rate. For example, the oxygen-16 nucleus has a P:N ratio of 1:1.0, while that of uranium-238 has a P:N ratio of 1:1.6. Figure 1.1 shows a plot of P versus N for stable isotopes [2]. The figure uses the conventional symbol, Z, for the number of protons (from the German, Zahl, for “number” [3]). This need for ever-increasing proportions of neutrons to “stabilize” the nucleus has major implications for superheavy element synthesis as will be shown later in this chapter.
Figure 1.1 Plot of neutrons to protons in stable nuclei (adapted from Ref. [2]).
Nuclear Spin Pairing
Different from electron behavior, spin pairing is an important factor for nucleons. In fact, of the 273 stable nuclei, 54% have even numbers of both protons and neutrons (Table 1.1). There is similarly a predominance of even–even nuclei for long-lived radioactive isotopes; those that date back to the origins of the elements [4]. Only four stable nuclei have odd numbers of both protons and neutrons. These stable odd–odd nuclei are hydrogen-2, lithium-6, boron-10, and nitrogen-14 [1]. The only four long-lived odd–odd radioactive isotopes are potassium-40, vanadium-50, lanthanum-138, and lutetium-176.
Table 1.1 Distribution of isotopes
Spin pairing increases the binding energy; thus, an odd–odd combination has a weaker binding energy than other nuclei, especially even–even. If we look at a series of atoms with the same nucleon (mass) number but differing numbers of protons and neutrons, known as isobars, an interesting pattern emerges, known as the Mattauch Isobar Rule:
The Mattauch Isobar Rule states that: if two adjacent elements in the Periodic Table have isotopes of the same nucleon number, then at least one of the isobars must be a radionuclide (i.e., radioactive).
This phenomenon is illustrated by the “triplet” isobars, argon-40, potassium-40, and calcium-40, where the argon and calcium isotopes are both stable, while the intervening isobar of potassium is radioactive.
The lack of any stable isotopes of technetium and promethium have always been a notable feature of the Periodic Table. Johnstone et al. have used the Mattauch Isobar Rule as a justification of the instability of all technetium isotopes [2]. The neighbors on either side, molybdenum and ruthenium, have six and seven stable isotopes, respectively. These isotopes span the range of “normal” P:N ratios, thus precluding any technetium isotope having a possibility of existence within that range.
The underlying phenomenon was discussed by Suess. He accounted for the instabilities for both technetium and promethium as follows [5]:
After the filling of the 50- and 82-neutron shell [see discussion below], an upward shift in the β decay energies occurs equivalent to the drop in the binding
