Energy-level diagram: Bohr

Figure 4.S The energy-level diagram from the Bohr model provides an explanation of the Bahner series. Not drawn to scale.

Bohr theory (4.2) build-up principle (4.4) degenerate (4.4) discrete energy levels (4.2) electromagnetic spectrum (4.1) electronic configuration (4.5) energy level diagram (4.7) excited state (4.3) frequency (4.1) ground state (4.3)... 

The Bohr model thus predicts a discrete energy-level diagram for the one-electron atom (Figs. 4.12 and 4.13). The gronnd state is identified by n = 1, and the excited states have higher values of n (see Fig. 4.12). 

Figure 6.10 I In the Bohr model, electrons move between allowed orbits when an atom absorbs or emits hght. Important elements of this model, including the idea of fixed orbital paths, are not correct. But it played an essential role in the development of our understanding of atomic stmcture. Note the similarity between this figure and the energy level diagram we used in Example Problem 6.4 both reflect the concept that electrons in atoms are restricted to certain allowed energies.

The energy-level diagram for the hydrogen atom is shown in Figure 5-9. The energy of the atom in the /tth stationary state is given in the Bohr theory by the equation... 

Figure 7.9 Electronic transitions in the Bohr model for the hydrogen atom, (a) An energy-level diagram for electronic transitions, (b) An orbit-transition diagram, which accounts for the experimental spectrum. (Note that the orbits shown are schematic. They are not drawn to scale.) (c) The resulting line spectrum on a photographic plate is shown. Note that the lines in the visible region of the spectrum correspond to transitions from higher levels to the n = 2 level.

The following is an energy-level diagram for electronic transitions in the Bohr hydrogen atom. 

As shown in Figure 2.9A, a common way to show the arrangement of electrons in an atom is to draw circles around the atomic symbol. Each circle represents an energy level. Dots represent electrons that occupy each energy level. This kind of diagram is called a Bohr-Rutherford diagram. It is named after two scientists who contributed their insights to the atomic theory. 

A) A Bohr-Rutherford diagram (B) Hydrogen and helium have a single energy level. (C) The eight Period 2 elements have two energy levels. 

It is time-consuming to draw electron arrangements using Bohr-Rutherford diagrams. It is much simpler to use Lewis structures to represent elements and the valence electrons of their atoms. To draw a Lewis structure, you replace the nucleus and inner energy levels of an atom with its atomic symbol. Then you place dots around the atomic symbol to represent the valence electrons. The order in which you place the first four dots is up to you. You may find it simplest to start at the top and proceed clockwise right, then bottom, then left. 

Here again, therefore, we obtain for our term scheme an equidistant succession of energy levels, as in Bohr s theory. The sole difference lies in the fact that the whole term diagram of quantum mechanics is displaced relative to that of Bohr s theory by half a quantum of energy. Although this difference does not manifest itself in the spectrum, it plays a part in statistical problems. In any case it is important to note that the linear harmonic oscillator possesses energy hv in. the lowest state, the so-called zem-jpoint energy. 

Fig. 15. Calculated and observed excited state energy levels of Cs2U02Cl4. The symmetries indicated at the right of the diagram are in Dih. The numbers associated with the levels are magnetic moments in Bohr magnetons from Ref. [40]...

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