Mass parabola

Figure 7.4 Mass parabolas for some members of the An + 3 natural decay series. The main decay path is shown by a solid line while a weak branch is indicated by a dashed line.

The natural decay series starting with 232Th has the sequence a(3(3a. Show why this is the case by plotting the mass parabolas (or portions thereof) for A = 232, 228, and 224. 

In the case of A = 128, there are two stable nuclides, Te and Xe. I has a choice of destination, and 93.1 % decays by to Xe and 6.98 % decays by EC to Te. The dominance of the Xe transition reflects the greater energy release, as indicated in Figure 1.12. This behaviour is quite common for even mass parabolas and this choice of decay mode is available for such well-known nuclides as and Eu. Occasionally, if the decay energy for is sufficient, a nuclide will decay sometimes by and sometimes by EC and... 

Since shallow-level impurities have energy eigenvalues very near Arose of tire perfect crystal, tliey can be described using a perturbative approach first developed in tire 1950s and known as effective mass theoiy (EMT). The idea is to approximate tire band nearest to tire shallow level by a parabola, tire curvature of which is characterized by an effective mass parameter m. ... 

In turbulent flow, properties such as the pressure and velocity fluctuate rapidly at each location, as do the temperature and solute concentration in flows with heat and mass transfer. By tracking patches of dye distributed across the diameter of the tube, it is possible to demonstrate that the liquid s velocity (the time-averaged value in the case of turbulent flow) varies across the diameter of the tube. In both laminar and turbulent flow the velocity is zero at the wall and has a maximum value at the centre-line. For laminar flow the velocity profile is a parabola but for turbulent flow the profile is much flatter over most of the diameter. 

Most practitioners of the precise art and subtle science of mass spectrometry acknowledge the field to have originated with the work of J.J. Thomson (Fig. 19.1) and associates, [6] published in 1910-1912, using the parabola mass spectrograph. Seminal discoveries that he and his coworkers made include the fact that the elements could be polyisotopic, by discovering the isotopes of neon. Thomson was awarded the Nobel Prize in physics of 19062 for his work on investigations on the conduction of electricity by gases. ... 

Figure 1.5 Parabola mass spectrograph constructed bylJ. Thomson (1910) with a discharge tube as ion source, a superimposed electrical field and a magnetic field oriented parallel to it for ion separation, and a photoplate for ion detection. (H. Kienitz (ed.), Massenspektrometrie (1968), Verlag Chemie, Weinheim. Reproduced by permission of Wiley-VCH.)...

In several experiments Thomson also introduced molecules such as COCl2 and hydrocarbons into the discharge ion source of the parabola mass spectrograph and observed the formation of... 

THOMSON PARABOLA METHOD. The method of investigating the charge-to-mass ratio of positive ions in which the ions are acted upon by electric and magnetic fields applied in the same direction normal to the path of the ions. It can be shown that ions of a given charge-to-mass ratio but different velocities will be deflected so as to form a parabola. 

Thus, the mass equation at constant A takes on the form of a parabola (a + (3Z + yZ2) in Z. The third term, y, is positive, and so the parabola goes through a minimum for some value of Z, which is termed ZA. Note that ZA is not necessarily an integer. We can now ask ourselves what is the value of ZA We can evaluate this by minimizing M with respect to Z at constant A, that is, we get a simple partial differential equation ... 

It should be emphasised that in general initial portions of the x-t and y - t dependences are not parabolic. Nonetheless, in the case under consideration some initial portion of the time dependence of the total thickness of both layers is close to a parabola. This portion (from 0 to about 400 s) can be described with fairly good accuracy by the parabolic equation x = 2k t, where k = (8 2)xl0 m s. From a formal viewpoint, it can therefore be concluded (especially if only the dependence of the total thickness or mass of both compound layers upon time is analysed) that the parabolic growth law gradually transforms into the linear growth law, whereas the layer-growth kinetics are in fact somewhat more complicated. 

Only if there were a transfer of, say, an H+, H, or H in a reaction, AH + B - A + HB (charges not indicated), at a fairly large AB separation distance, would the situation be rather analogous to that of ETs. The H transfer would occur at an approximately fixed position of A and B, fixed because of the substantially larger masses of A and B compared with that of H. That is, an approximate version of the Franck-Condon principle would apply. Under such conditions of an H transfer, the description of the reaction via two intersecting approximate parabolas would be a reasonable first approximation. 

J.J. THOMSON constructs the first mass spectrometer (then called a parabola spectrograph) [16], He obtains mass spectra of O2, N2, CO, CO2 and COCI2. He observes negative and multiply charged ions. He discovers metastable ions. In 1913, he discovers isotopes 20 and 22 of neon. 

The existence of He was first estabished by Hiby ° in 1939 when he observed H2 and He in canal rays from hydrogen and helium with a parabola mass spectograph Although Dopel had reported the He species earlier,... 

Potential energy diagrams for diatomic molecules were introduced in Section 3.5, and you can see that they are not parabolic over the entire region 0 < r < 00 (for example, see Fig. 3.9). Near the equilibrium internuclear separation the potential appears to be well approximated by a parabola. This similarity suggests that the harmonic oscillator should be a good model to describe the vibrations of diatomic molecules. The dependence of the vibrational frequency v on the force constant k and the mass has the same form as Equation 4.44, but now the mass is the reduced mass /t of the two nuclei... 

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