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 Z. Moseley's empiric formula was found to be derivable from Rydberg and Bohr's formula (Moseley actually mentions only Ernest Rutherford and Antonius Van den Broek in terms of models).
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It was not until the work of Henry Moseley working with the Bohr model of the atom with the explicit idea of testing van den Broek's theory, that it was realized that atomic number was indeed a purely physical property (the charge of the nucleus) which could be measured, and that van den Broek's original guess had been correct, or very close to correct.
Proposed in 1876, it perfectly predicted the wavelengths of the Lyman series, but lacked a theoretical basis until Niels Bohr produced his Bohr model of the atom in 1925.
Jimmy Wales of Wikipedia is one of the three celebrities who were awarded the medal for 2013 at an event in honour of the 100th anniversary of Bohr's atomic model.
An explanation for this phenomenon is provided by the Bohr model, according to which the energy levels of electron orbitals in a hydrogen atom are inversely proportional to square unit fractions, and the energy of a photon is quantized to the difference between two levels.