48-2 X RAYS AND THE NUMBERING OF THE ELEMENTS This agrees with the experimental result labeled Amin in Fig. 48-1. (Note that the quantity in the second set of parentheses in the denominator is a conversion factor.) 48-2 X RAYS AND THE NUMBERING OF THE ELEMENTS From the time of Mendeleev (1834-1907) the elements were listed in the periodic table in the order of increasing atomic weight. One difficulty was that, in several cases, the strict order of increasing atomic weights had to be reversed to maintain the similarity of chemical properties in the vertical columns of the table. The young British physicist H. G. J. Moseley, whose promising research career was cut short at age 27 by a sniper's bullet in World War I, first introduced the concept of atomic number (symbol Z) and showed that these difficulties were removed if the periodic table was organized in order of increasing Z. In effect, Moseley showed how to string the elements in a line and to assign place numbers to them. His method was based on the measurement and analysis of the characteristic x rays of the elements. In his investigations, Moseley measured the wavelengths of the characteristic x rays of as many elements as he could find (he found 38), using them as targets for electron bombardment in an x-ray tube of his own design. He then sought, and readily found, regularities in the spectra as he moved from element to element in the periodic table. In particular he noted that if, for a given x-ray spectrum line such as Kai he plotted the square root of its frequency (=√f = √c/A) against the position of the associated element in the periodic table, a straight line resulted. Figure 48-4 shows a portion of his data. Mosely's conclusion from the full body of his data was:
We have here a proof that there is in the atom a fundamental quantity, which increases by regular steps as we pass from one element to the next. This quantity can only be the charge on the central atomic nucleus. Thus did Moseley discover the concept, and the physical significance, of atomic number. Moseley's data, shown in Fig. 48-4, can be represented by the linear relation √f =C(Z-1), (48-2) √f =C(Z-1), (48-2) in which C is a constant and Z is the numerical position of the element in the periodic table. This equation, which can be derived from Bohr's hybrid quantum theory, fits the data very well. Moseley's achievement can be appreciated al) the more when we realize the state of understanding of atomic structure at that time (1913). The nuclear model of the atom had been proposed by Rutherford only two years earlier. Little was known about the magnitude of the nuclear charge or
Figure 48-4. A Moseley plot of the Ka line of the x-ray spectrum of 21 elements. The frequency is determined from the measured wavelength.Figure 48-4. A Moseley plot of the Ka line of the x-ray spectrum of 21 elements. The frequency is determined from the measured wavelength.
about the arrangement of the atomic electrons. Quantum mechanics had yet to be discovered. The periodic table had several empty squares, and a surprisingly large number of claims for new elements had been advanced. The rare earth elements, because of the problems caused by their similar chemical properties, had not yet been properly sorted out. Due to Moseley's work, the characteristic x-ray spectrum became the universally accepted signature of an element. It is not hard to see why the characteristic x-ray spectrum shows such remarkable regularities from element to element whereas the visible spectrum does not. The key to the identity of an clement is the charge on its nucleus. This determines the number of its atomic electrons and thus its chemical properties. Gold, for example, is what it is because its atoms have a nuclear charge of + 79e. If it had one more unit of charge, it would not be gold but mercury; if it had one less, it would be platinum. The if-shcll electrons, which play such a large role in the generation of the characteristic x-ray spectra, lie very close to the nucleus and are sensitive probes of its charge. The visible spectrum, on the other hand, is associated with transitions of the outer electrons, which are heavily shielded or "screened" from the nucleus by the remaining atomic electrons; they are not sensitive probes of nuclear charge. Bohr Theory and the Moseley Plot Bohr's theory works well for hydrogen but fails for atoms with more than one electron (in part because it docs not include the repulsive interaction between the electrons).