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 In general, how should the energy of an element's La X rays compare with the energy of its \(K \alpha\) X rays? a. They have less energy. b. They have the same energy. c. They have greater energy. d. You can't tell without knowing the element.

Step by step solution

01

Understanding atomic shells and transitions

The atomic shells are generally categorized as K, L, M, N shells and so on, moving from innermost (nucleus side) to the outermost of the atom. Each shell has a specific energy level associated with it and higher shells have greater energy levels compared to lower shells.

02

Discussing L to K shell transition

When an electron transitions from the L shell to the K shell (noted as \(K \alpha\)), it traverses from a higher energy level to a lower one. This transition results in the emission of a photon, which forms the characteristic X Ray. The energy of this photon (and hence the X-ray) is equal to the difference between the L and K shell energy levels.

03

Discussing internal transitions within the L shell

The characteristic X-ray noted as \(L \alpha\) involves a transition within the L shell itself, i.e., from a higher energy orbit in the L shell to a lower energy one. Here, the energy difference of the two orbits, hence the emitted photon energy, is less than the difference between L and K shells' energy.

04

Comparison of energies of the X-rays

As we determined in steps 2 and 3, the energy of the X-ray photon corresponds to the energy difference between the electron orbits. Since K shell has lower energy than L shell, the energy difference is greater, and hence \(K \alpha\) X-rays have more energy compared to \(L \alpha\) X-rays.

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