Editing Bohr model (section)

== Moseley's law and calculation (K-alpha X-ray emission lines) ==
Niels Bohr said in 1962: "You see actually the Rutherford work was not taken seriously. We cannot understand today, but it was not taken seriously at all. There was no mention of it any place. The great change came from Moseley."<ref>{{Cite interview |last=Bohr |first=Niels |subject-link=Niels Bohr |interviewer1=Thomas S. Kuhn |interviewer2=Leon Rosenfeld |interviewer3=Aage Petersen |interviewer4=Erik Rudinger |title=Niels Bohr – Session I |url=https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4517-1 |publisher=American Institute of Physics |date=31 October 1962}}</ref>

In 1913, [[Henry Moseley]] found an empirical relationship between the strongest X-ray line emitted by atoms under electron bombardment (then known as the [[K-alpha]] line), and their atomic number {{math|''Z''}}. Moseley's empiric formula was found to be derivable from Rydberg's formula and later Bohr's formula (Moseley actually mentions only Ernest Rutherford and [[Antonius Van den Broek]] in terms of models as these had been published before Moseley's work and Moseley's 1913 paper was published the same month as the first Bohr model paper).<ref>{{Cite journal |last=Moseley |first=H.G.J. |date=1913 |title=The high-frequency spectra of the elements |url=https://archive.org/stream/londonedinburg6261913lond#page/1024/mode/2up |journal=Philosophical Magazine |series=6th series |volume=26 |pages=1024–1034}}</ref> The two additional assumptions that '''[1]''' this X-ray line came from a transition between energy levels with quantum numbers 1 and 2, and '''[2]''', that the atomic number {{math|''Z''}} when used in the formula for atoms heavier than hydrogen, should be diminished by 1, to {{math|(''Z''&nbsp;−&nbsp;1)<sup>2</sup>}}.

Moseley wrote to Bohr, puzzled about his results, but Bohr was not able to help. At that time, he thought that the postulated innermost "K" shell of electrons should have at least four electrons, not the two which would have neatly explained the result. So Moseley published his results without a theoretical explanation.

It was [[Walther Kossel]] in 1914 and in 1916 who explained that in the periodic table new elements would be created as electrons were added to the outer shell. In Kossel's paper, he writes: "This leads to the conclusion that the electrons, which are added further, should be put into concentric rings or shells, on each of which ... only a certain number of electrons—namely, eight in our case—should be arranged. As soon as one ring or shell is completed, a new one has to be started for the next element; the number of electrons, which are most easily accessible, and lie at the outermost periphery, increases again from element to element and, therefore, in the formation of each new shell the chemical periodicity is repeated."<ref name=Kossel1916/><ref name=Kragh2012/> Later, chemist Langmuir realized that the effect was caused by charge screening, with an inner shell containing only 2 electrons. In his 1919 paper, [[Irving Langmuir]] postulated the existence of "cells" which could each only contain two electrons each, and these were arranged in "equidistant layers".

In the Moseley experiment, one of the innermost electrons in the atom is knocked out, leaving a vacancy in the lowest Bohr orbit, which contains a single remaining electron. This vacancy is then filled by an electron from the next orbit, which has n=2. But the n=2 electrons see an effective charge of ''Z''&nbsp;−&nbsp;1, which is the value appropriate for the charge of the nucleus, when a single electron remains in the lowest Bohr orbit to screen the nuclear charge +''Z'', and lower it by −1 (due to the electron's negative charge screening the nuclear positive charge). The energy gained by an electron dropping from the second shell to the first gives Moseley's law for K-alpha lines,
: <math>E = h\nu = E_i-E_f=R_\mathrm{E} (Z-1)^2 \left( \frac{1}{1^2} - \frac{1}{2^2} \right),</math>
or
: <math>f = \nu = R_\mathrm{v} \left( \frac{3}{4}\right) (Z-1)^2 = (2.46 \times 10^{15}~\text{Hz})(Z-1)^2.</math>

Here, '''''R''<sub>v</sub>''' = '''''R''<sub>E</sub>/''h''''' is the Rydberg constant, in terms of frequency equal to 3.28 x 10<sup>15</sup> Hz. For values of Z between 11 and 31 this latter relationship had been empirically derived by Moseley, in a simple (linear) plot of the square root of X-ray frequency against atomic number (however, for silver, Z = 47, the experimentally obtained screening term should be replaced by 0.4). Notwithstanding its restricted validity,<ref>{{Cite journal |last=M.A.B. Whitaker |year=1999 |title=The Bohr–Moseley synthesis and a simple model for atomic x-ray energies |journal=[[European Journal of Physics]] |volume=20 |issue=3 |pages=213–220 |bibcode=1999EJPh...20..213W |doi=10.1088/0143-0807/20/3/312 |s2cid=250901403}}</ref> Moseley's law not only established the objective meaning of atomic number, but as Bohr noted, it also did more than the Rydberg derivation to establish the validity of the Rutherford/Van den Broek/Bohr nuclear model of the atom, with atomic number (place on the periodic table) standing for whole units of nuclear charge. Van den Broek had published his model in January 1913 showing the periodic table was arranged according to charge while Bohr's atomic model was not published until July 1913.<ref>{{Cite journal |last=van den Broek |first=Antonius |author-link=Antonius van den Broek |date=January 1913 |title=Die Radioelemente, das periodische System und die Konstitution der. Atome |url=https://babel.hathitrust.org/cgi/pt?id=mdp.39015021268936&view=1up&seq=66 |journal=[[Physikalische Zeitschrift]] |volume=14 |pages=32–41 |language=de}}</ref>

The [[K-alpha]] line of Moseley's time is now known to be a pair of close lines, written as ('''Kα<sub>1</sub>''' and '''Kα<sub>2</sub>''') in [[Siegbahn notation]].