![]() ![]() In 1914 it was realized that Moseley's formula could be adapted from Bohr's, if two assumptions were made. However, for hydrogenic atoms (those in which the electron acts as though it circles a single structure with effective charge Z), Bohr realized from his derivation that an extra quantity Z 2 would need to be added to the conventional q e 4, in order to account for the extra pull on the electron, and thus the extra energy between levels, as a result of the increased nuclear charge. That is, the hydrogen nucleus contains a single charge. It is assumed that the final energy level is less than the initial energy level.įor hydrogen, the quantity because Z (the nuclear positive charge, in fundamental units of the electron charge q e) is equal to 1. = charge of an electron (1.60 × 10 −19 coulombs) The energy of photons that a hydrogen atom can emit in the Bohr derivation of the Rydberg formula, is given by the difference of any two hydrogen energy levels: Using the derived formula for the different 'energy' levels of hydrogen one may determine the energy or frequencies of light that a hydrogen atom can emit. When the electron moves from one energy level to another, a photon is given off. The 19th century empirically-derived Rydberg formula for spectroscopists is explained in the Bohr model as describing the transitions or quantum jumps between one energy level and another in a hydrogen atom. However, at the time Moseley derived his laws, neither he nor Bohr could account for their form. However, it was almost immediately noted (in 1914) that his formula could be explained in terms of the newly postulated 1913 Bohr model of the atom (see for details of derivation of this for hydrogen), if certain reasonable extra assumptions about atomic structure in other elements were made. Moseley derived his formula empirically by plotting the square root of X-ray frequencies against a line representing atomic number. Thus, Moseley's two given formulae for K-alpha and L-alpha lines, in his original semi-Rydberg style notion, (squaring both sides for clarity), are:ĭerivation and justification from the Bohr model of the Rutherford nuclear atom Moseley found the entire term was (Z - 7.4) 2 for L-alpha transitions, and again his fit to data was good, but not as close as for K-alpha lines. Moseley's was given as a general empiric constant so that it could be used to fit X-ray L-alpha transition lines (these are weaker-intensity and lower frequency lines found in all X-ray element spectra), and in which case the additional numerical factor to modify Z is much higher. Moseley himself (see his on-line paper below) chose to show this without per se, which instead was given by Moseley as a pure constant number in the standard Rydberg style, as simply 3/4 (that is, 1- 1/4) of the fundamental Rydberg frequency (3.29*10 15 Hz) for K-alpha lines, and (again) for L-alpha lines according to the Rydberg formula, where must be 1/4 - 1/9 = 5/36 times the Rydberg frequency this also was the way Moseley chose to write it. Is the frequency of the main or K x-ray emission lineĪnd are constants that depend on the type of lineįor example, the values for and are the same for all K α lines (in Siegbahn notation), so the formula can be rewritten thus: Moseley found that this relationship could be expressed by a simple formula, later called Moseley's Law. ![]() ![]() Using x-ray diffraction techniques in the 1910s, Henry Moseley found that the most intense short-wavelength line in the x-ray spectrum of a particular element was related to the element's atomic number, Z. 2 Derivation and justification from the Bohr model of the Rutherford nuclear atom. ![]()
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