Moseley's Law

Moseley's measurements. In 1913, Henry Moseley, using an X-ray diffraction spectrometer, systematically measured the wavelength (and hence the frequency) of the characteristic $K_\alpha$ X-ray line (Section 1.8) produced by a large number of different elements used, in turn, as the target of a Coolidge tube. Plotting the SQUARE ROOT of the measured frequency, $\sqrt{\nu}$, against each element's position in the periodic table, he found the points fell -- to striking accuracy -- on a single straight line.

Statement of the law. This relationship, known as Moseley's law, is written

where $\nu$ is the frequency of the characteristic X-ray line concerned, $Z$ is the ATOMIC NUMBER of the target element, and $a$ and $b$ are constants: $a$ depends only on which characteristic LINE is being measured (the same for every element, for a given line such as $K_\alpha$), while $b$, called the screening constant, accounts for the fact that the nucleus's full charge $Ze$ is not felt by the transitioning electron undiminished -- it is partly "screened" (shielded) by the OTHER electron(s) still present in the inner shells. For the $K_\alpha$ line specifically, only one electron remains in the K-shell during the transition, so $b\approx1$, giving

a form that follows directly from treating the $K_\alpha$ transition as a Lyman-alpha-like ($n=2\to n=1$) jump in a hydrogen-like ion of EFFECTIVE nuclear charge $(Z-1)e$ rather than the full $Ze$ (Numerical 8 uses this formula directly).

Why this mattered -- fixing the periodic table. Before Moseley's work, elements in the periodic table were ordered by increasing ATOMIC MASS, since atomic number as a distinct physical quantity had no direct experimental measurement of its own -- it was merely inferred from an element's assumed position. This mass-based ordering created a handful of stubborn anomalies, where following atomic mass strictly placed an element in the wrong chemical family: cobalt (atomic mass $58.93$) had to be placed BEFORE nickel (atomic mass $58.69$), even though cobalt's mass is slightly LARGER; similarly argon ($39.95$) had to precede potassium ($39.10$), and tellurium ($127.60$) had to precede iodine ($126.90$) -- in each case, strict mass ordering would have put the elements in the chemically wrong order. Moseley's measurements gave, for the first time, a direct PHYSICAL determination of each element's true atomic number $Z$, independent of its chemical behaviour or measured mass altogether -- and in every one of these anomalous cases, ordering strictly by the measured $Z$ (not mass) placed the elements exactly where their chemistry said they belonged, resolving the anomalies decisively and confirming that atomic number, not atomic mass, is the correct fundamental basis for the periodic table's arrangement. …