E. Lazzarini and M. Mandelli Bettoni lstituto di lngegneria Nucleare Politecnico Via Ponzio, 34/3 20133 Milano, Italy
Teaching Moseley's Law
I
This paper describes a classroom experiment, designed for first-year students of radiochemistry and atomic physics a t the Milan Polytechnic School of Engineering, to test the fundamental Moseley law. Modem instrumentation, indeed, makes it possible to achieve this aim in a quite reasonable time (4-5 hr). Moreover, the experiment offers the opportunity to introduce the method of elemental chemical analysis by X-ray fluorescence and, after a discussion of the influence of the outer electrons on the screening constant, the principles of electron spectroscopy for chemical analysis (ESCA) ( I ) and the chemical shift in Mosshauer spectra can also be described (2). Introduction to Moseley's Law
When an atom absorbs a suitable amount of energy by interaction with a photon or with an electron, the atom suffers ionization in its inner shells, for instance the K shell, and, as a consequence, an electron of the outer shells makes a transition to the inner vacant quantum state. The transition is accompanied by the emission of an X-ray photon.' The X-ray photons are classified in terms (1) of the shell in which the hole is produced, and (2) of the shell from which the electron making the transition starts. For instance, K and L lines arise when the hole is formed on the K and L shells, respectively; if the hole in the K shell is filled by an electron coming from the L or M shell. Kcu or K8 X-ravs are emitted. res~ectivelv. In ~ i g u r e1 the electron transitions giving rise'to the Kcr and Kd lines are era~hicallv It may be oh- . . represented. . served'that numerous level combinations are missing in the scheme; indeed, the selection rules for the optical transitions are also valid for the X-ray emission; thus, for instance, only p, but not s or d electrons, can fill a hole in the K shell because of the selection rule for the azimuthal quantum number (A1 = + 1). In 1913, Moseley (3) published his famous paper in which it was stated that the square root of the wave number (that is the energy) of the Kcr photons emitted by an element is linearly correlated with the number Z of the place occupied by this element in Mendeleev's periodic classification of the elements. Nowadays, Z is called the atomic number. In other words, Moseley found that the energies of the X-ray photons emitted in electronic transitions of the same type are related to Z by an equation of the following kind ( h V y = Q.Y(Z- c . ~ ) (1)
A c~assroomexperiment W, but Mendeleev himself recognized that when the atomic weight order demanded a n incongruous location of the element in the periodic system, the criterion of the atomic weight must he sacrified. Thus Mendeleev classified A, Co, and Te before and not after K , Ni, and I, respectively. Two hypotheses could be advanced in order to justify this arbitrariness, which departed from the atomic weight principle: the atomic weights were either wrong, or the atomic weight criterion was not the fundamental one of chemical periodicity. Mendeleev's feeling was for the former hypothesis, but successive redeterminations of the atomic weights of A, K, Co, Ni, Te, and I substantially confirmed the previous atomic weight determination. As the classification of the elements according to the increasing energy of the Kn lines also ranked A before K, Co before Ni, and Te before I, Moseley concluded that his experiment led to the view that the correct parameter for the classification of the elements was not the atomic weight, but the number of unit electric charges Z on the atomic nucleus as reflected by the place occupied by the elements in Mendeleev's periodic system. This hypothesis could he definitely supported by absolute measurements of the nuclear charge. Seven years later (1920), Chadwick (4) succeeded in measuring directly the nuclear charge for copper, silver, and platinum by rr particle scattering, and the following values were obtained: Zc, = 29.3 0.5; Zn, = 46.3 + 0.7; Z,,, = 77.4 1. These results are not accurate enough to determine unique integral values of Z, hut they do give a definitive proof of Moseley's point of view. The theoretical interpretation of Moseley's law became
*
where: the index X refers to the type of X-ray transition (e.g., Kn, KO, Ln, etc.); Qx is a constant different for the different types of transition; ox is also a constant, the screening constant, related to the kind of X-ray transition. Specifically, Moseley suggested a K , = 1 and o ~ .= 7.4 for the elements up to Z values of about 40. It is worth noting that the Mendeleev classification of the elements was based on the periodicity of the chemical properties of the elements a t increasing atomic weights -
'The de-excitation bv emission of an Aueer electron can be disFigure 1. K X-Ray transitions arising from L and M shells
454 / Journal of Chemical Education
possible two years after the puhlication of Moseley's paper, when Bohr published his famous work "On the quantum theory of radiation and the structure of the atom" (5). According to Bohr's theory, the binding energy of the last electron remaining to an atom of atomic number Z, ionized ( Z - 1) times, is given by
where e and rn are the electron charge and mass, respectively; h is the Planck constant; t. the dielectric constant in uacuo, and n the principal quantum number of the atomic level in which only this electron stays. In a neutral atom with a high value of Z (6), the 1s electrons are closer to the nucleus than the remaining (Z - 2) electrons; thus, the 1s electrons have binding energies almost as if the outer ( Z - 2) electrons had been removed from their shells. Therefore, the binding energy of each 1s electron can he roughly calculated from eqn. (2), in which Z is replaced by (Z - 1) in order to take into account repulsion hy the other 1s electron. Similarly, when one 1s electron is removed from the K shell, the hinding energy of each 2p electron can he calculated from eqn. (2) by replacing Z with ( Z - 1) and by putting n = 2. Thus, when a 2p electron undergoes the transition to a hole in the K shell (K
