The radius of trajectory is proportional to the square root of the mass-to-I charge ratio, m/e, as follows . / [Pg.48]

Fig. IV-25. The evaporation resistance multiplied by the square root of temperature versus area per molecule for monolayers of octadecanol on water illustrating agreement with the accessible area model. (From Ref. 290.) |

The simplest way to obtain X is to diagonalize S, take the reciprocal square roots of the eigenvalues and then transfomi the matrix back to its original representation, i.e. [Pg.39]

As is the case for the double coincidence arrangement 8 is inversely proportional to the square root of [Pg.1435]

The diagonal elements of this matrix approximate the variances of the corresponding parameters. The square roots of these variances are estimates of the standard errors in the parameters and, in effect, are a measure of the uncertainties of those parameters. [Pg.102]

In the simplest fomi, reflects the time of flight of the ions from the ion source to the detector. This time is proportional to the square root of the mass, i.e., as the masses of the ions increase, they become closer together in flight time. This is a limiting parameter when considering the mass resolution of the TOP instrument. [Pg.1351]

As in tire case of themial conductivity, we see that the viscosity is independent of the density at low densities, and grows witli the square root of the gas temperature. This latter prediction is modified by a more systematic calculation based upon the Boltzmaim equation, but the independence of viscosity on density remains valid in the Boltzmaim equation approach as well. [Pg.675]

Show that for the case of a liquid-air interface Eq. XIII-8 predicts that the distance a liquid has penetrated into a capillary increases with the square root of the time. [Pg.489]

Finally, one problem still remains. There are complex temis which need to be associated with the detemimant. The complex temis (Maslov indices) have to do with the square root of tlie detenninant, which may be negative, and also appear in the related WKB approximation. They can be calculated, albeit with difficulty [Pg.2315]

Figure 9. Energy difference (absolute value) between the components of the X II electronic State of HCCS as a function of coordinates p, P2, and y. Curves represent the square root of the second of functions given by Eq. (77) (with e, = —0.011, 2 = 0.013, 8,2 = 0.005325) for fixed values of coordinates p, and P2 (attached at each curve) and variable Y = 4>2 Here y = 0 corresponds to cis-planar geometry and y = 71 to trans-planar geometry. Symbols results of explicit ab initio calculations. |

A conical intersection needs at least two nuclear degrees of freedom to form. In a ID system states of different symmetry will cross as Wy = 0 for i j and so when Wu = 0 the surfaces are degenerate. There is, however, no coupling between the states. States of the same symmetry in contrast cannot cross, as both Wij and Wu are nonzero and so the square root in Eq. (68) is always nonzero. This is the basis of the well-known non-crossing rule. [Pg.286]

Barnes and Hunter [290] have measured the evaporation resistance across octadecanol monolayers as a function of temperature to test the appropriateness of several models. The experimental results agreed with three theories the energy barrier theory, the density fluctuation theory, and the accessible area theory. A plot of the resistance times the square root of the temperature against the area per molecule should collapse the data for all temperatures and pressures as shown in Fig. IV-25. A similar temperature study on octadecylurea monolayers showed agreement with only the accessible area model [291]. [Pg.148]

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