Whole-number rule

F. W. Aston (Cambridge) discovery, by means of the mass spectrograph, of isotopes in a large number of non-radioactive elements and for enunciation of the whole-number rule. 

Aston, the Mass Spectrograph, the Whole Number Rule... 

Another piece of information was necessary before one arrives at a periodic table which is close to the modern view. This is the whole number rule which states that the masses of atoms on the 160 scale (i.e. mass of the major isotope of oxygen is 16.00) tend to have close to integer values. This information was provided by W. D. Harkins (vide infra) and F. W. Aston (Historical Vignette 1.2). 

There is anecdotal material that W. D. Harkins, whose career at the University of Chicago started around the time of World War I, felt that his scientific contributions were not adequately recognized by the community. It is indeed correct that he is not well known for his contributions to the Whole Number Rule . 

HW noted that past atomic number 27 the whole number rule did not work for the atomic weights. They attributed this fact either to the presence of isotopes for all of these elements or to some phenomenon which they did not understand. The first explanation (isotopes) is correct. The mass spectrograph, already mentioned as an invention of Aston, shows that all isotopic masses on the 160 scale (or the very similar 12C scale used today) tend to differ from integer values by less than 0.1%. 

Of more relevance, in the present context, HW reasoned that large deviations from the whole number rule among the light elements indicates the existence of isotopes. They, thus, predicted that Mg, Si, and Cl had isotopes (were not mono-isotopic). Harkins decided to show that the element chlorine which had the atomic weight deviating the most from integer value among the 27 low atomic number... 

Aston, F. W. A new spectrograph and the whole number rule. Proc. Roy. Soc. Land. A115,487-514 (1927). 

ASTON WHOLE NUMBER RULE The atomic weights of isotopes are (very nearly) whole numbers when expressed in atomic weight units, and the deviations from the whole numbers of the atomic weights of the elements are due to the presence of several isotopes with different weights. 

Although the concept of the atom has not been in serious question for nearly a half-century, full understanding of the forces that hold the neutrons and protons together has not yet been achieved. In 1927, Aston found that experimentally measured isotopic weights differed slightly from whole numbers. See also Aston Whole Number Rule. From this he was led to the concept of the packing fraction, which is defined as the... 

The whole number rule is not, and never was supposed to be, mathematically exact, for this would imply an identical packing effect in the ease of all atoms, an exceedingly improbable supposition. 1... 

Mass spectrographs were also built in the United States by A. J. Dempster and K. T. Bainbridge. The mass spectrograph has been succeeded by the mass spectrometer, in which the intensity of the separated ion beams are measured electrically. These instruments are now widely used in the determination of molecular structure (Chapter 13). The term relative atomic mass is now used in place of atomic weight, and isotopic masses are measured on the = 12.0000 scale. Aston himself soon discovered that small deviations from the whole-number rule are the norm. 

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