With sufficient energy, it's possible to eject an electron from an inner atomic orbital. A higher-energy electron will then drop into the unoccupied state, emitting a photon with energy equal to the difference between the two levels. For inner-shell electrons, photon energies are in the keV range, putting them in the X-ray region of the spectrum. These characteristic X rays are labeled with the letter indicating the shell to which the electron drops, followed by a Greek letter indicating the higher level from which it drops; thus \(K \alpha\) designates a transition from the \(L\) shell to the \(K\) shell. Characteristic X rays provide scientists and physicians with an important diagnostic tool. Environmental scientists bombard pollution samples with high- energy electrons, knocking out inner-shell electrons and thus producing X-ray spectra that help identify contaminants (Fig. \(36.20 a\) ). Geologists do the same with rocks. Medical radiologists reverse the process, exploiting the fact that X rays cause inner-shell transitions as well as complete ejection of inner-shell electrons. In particular, radiologists use the element barium in this way to produce high-contrast X-ray images of the intestinal tract \((\text { Fig. } 36.20 b)\)(GRAPH CANNOT COPY) (a) An \(\mathrm{X}\) -ray spectrum from air pollutants trapped on a filter. The labeled peaks show the presence of lead (Pb) and arsenic (As), as evidenced by \(K \alpha, K \beta, L \alpha,\) and \(L \beta\) characteristic X rays. (b) \(\mathrm{X}\) -ray of an intestinal tract, made by coating the intestinal wall with X-ray-opaque barium Emission of characteristic \(X\) rays occurs in the context of multielectron atoms that generally have all but one of their electrons present. You should therefore expect the X-ray energies to be described a. quite accurately by Bohr's atomic theory. b. through hydrogen-like solutions to the Schridinger equation. c. only approximately by Bohr's or hydrogenic solutions to the Schrödinger equation.

Step by step solution

01

Analyze the options

Firstly, consider the three ways offered to explain the phenomenon:\n\na. Bohr's atomic theory\nb. Hydrogen-like solutions to the Schrödinger equation\nc. Approximate solutions to the Schrödinger equation by using Bohr's or hydrogenic solutions

02

Compare the characteristics of the theories

Secondly, consider the limitations of these theories. Bohr's atomic theory describes electron transitions well for hydrogen-like atoms (one-electron systems). On the other hand, Schrödinger's equation, when solved, provides a more general and exact understanding of multielectron atoms but it can get complex for larger atoms due to interactions between electrons.

03

Choose the appropriate theory

Looking at the problem which mentions 'multielectron atoms', it's clear that Bohr's model isn't the ideal one to describe the given scenario. However, the hydrogen-like solutions to the Schrödinger equation would also not be a completely accurate model due to the interactions between electrons in multielectron atoms. Therefore, QM solutions that include approximations are necessitated - those that maintain the idea of quantized energy levels, yet consider the complexity of electron-electron interactions found in such atoms.

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