Spectra energy levels, definition

The studies on [LaTb], [TbLu], [LaEr] and [CeY] established that the individual ions ofthe molecules [Tb2(HL)2(H2L)Cl(py)(H20)] and [CeEr(HL)2(H2L)(N03) (py)(H20)] exhibit isolated, well-defined ground state doublets, thus leading to proper definitions of qubit states. The next step is to prove the existence of a weak coupling within each molecule conducive to the appropriate energy level spectrum for the realization of quantum gate operations. 

Each line in an emission spectrum results from a transition between definite energy levels. Using the frequency or wavelength of each line, it is possible to calculate the energy difference between energy levels. 

Band emissions, on the other hand, are characteristic of excited molecules and a molecule, like an atom, can exist in a number of electronic energy levels. The change from one particular level to another results from the absorption or emission of a definite i.e. quantised) amount of energy. But, because of simultaneous changes which occur in the rotational or vibrational energy of the molecule, a series of closely spaced lines appear in the spectrum in the form of a band. 

Just as the Rutherford model of the atom developed in 1911 was scientifically startling with its revelation of the atom as mostly empty space, so was the Bohr model of the atom introduced in 1913 with its definition of the location of the electron within the atom. As Bohr and others realized that the atomic spectrum of each element is caused by electrons changing energy levels, a different picture of the atom emerged. The new picture of the atom had electrons at various energy levels within the empty space of Rutherford s model (Figure 8.6). This space can still be said to be empty because the mass of the electrons is extraordinarily small in comparison with that of the whole atom. 

Any of a number of lines corresponding to definite wavelengths of an atomic emission or absorption spectrum represents the energy difference between two energy levels. 

The line of thought followed so far may be summarized as follows. Classical mechanics, on the basis of the picture of the electron revolving round the nucleus, certainly enables us to deduce formula) for the connexion between orbital radius, frequency of revolution, and energy, but it is incapable of explaining the spectrum emitted by the atom. Tor the latter purpose we have, following Bohr, to introduce a new hypothesis, viz. that the atom only possesses certain definite energy levels Bn = and it is the business of the new mechanics to... 

When the hydrogen gas is placed in an external magnetic field, more lines appear in the spectrum, and these are accounted for by what is termed the Zeeman Effect . Under a magnetic influence, the plane of the electron orbit can be orientated in definite directions. The possible orientations can be associated with a fourth quantum number, which characterises the new f energy levels produced. It is known as the magnetic quantum number, m. This can take the values 0, 1, 2 etc. 

Most double resonance experiments exploit one of the four energy level schemes shown in Fig. 1.17. The variety of detection schemes is enormous, but most schemes may be divided into those which result in a signal on an essentially dark background vs. those which result in a dip in an essentially constant background level. By definition, the frequency of the PROBE (or DUMP) laser is scanned and that of the PUMP or DETECT laser is held fixed while a double resonance spectrum is being recorded. 

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