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Population ratio

When the light souree s intensity is so large as to render gBf i Af i (i.e., when the rate of spontaneous emission is small eompared to the stimulated rate), this population ratio reaehes (Bi f/Bf i), whieh was shown earlier to equal (gf/gi). In this ease, one says that the populations have been saturated by the intense light souree. Any further inerease in light intensity will result in zero inerease in the rate at whieh photons are being absorbed. Transitions that have had their populations saturated by the applieation of intense light sourees are said to display optieal transparency because they are unable to absorb (or emit) any further photons because of their state of saturation. [Pg.392]

By measuring the relative intensities of satellite and main lines, the population ratio is obtained, if it can be assumed that the dipole moment and line strength is not appreciably different in the two cases. From the population ratio R, the energy interval AE is obtained from the Boltzmann law i.e.,... [Pg.377]

Oosawa (1971) developed a simple mathematical model, using an approximate treatment, to describe the distribution of counterions. We shall use it here as it offers a clear qualitative description of the phenomenon, uncluttered by heavy mathematics associated with the Poisson-Boltzmann equation. Oosawa assumed that there were two phases, one occupied by the polyions, and the other external to them. He also assumed that each contained a uniform distribution of counterions. This is an approximation to the situation where distribution is governed by the Poisson distribution (Atkins, 1978). If the proportion of site-bound ions is negligible, the distribution of counterions between these phases is then given by the Boltzmann distribution, which relates the population ratio of two groups of atoms or ions to the energy difference between them. Thus, for monovalent counterions... [Pg.61]

Fig. 2.5.5 A study examining the conformational changes of the protein ubiquitin, showing the population ratio of the A-state to the native-state as a function of time, (a) The reaction from 0 to 120 s. (b) The reaction for the first 40 s, including curves fit to a single exponential. Reprinted with permission from Ref. [37]. Copyright (2003) American Chemical Society. Fig. 2.5.5 A study examining the conformational changes of the protein ubiquitin, showing the population ratio of the A-state to the native-state as a function of time, (a) The reaction from 0 to 120 s. (b) The reaction for the first 40 s, including curves fit to a single exponential. Reprinted with permission from Ref. [37]. Copyright (2003) American Chemical Society.
Evaluation of the Bronsted and Lewis site population ratio performed by XPS led to the ... [Pg.203]

Substituting the value for the population ratio 2/ i = 5.15 x 1CT9 derived from the intensity of the transitions in the Balmer series into Equation 4.4 allows the Balmer temperature to be calculated ... [Pg.99]

Barriers to Rotation and Population Ratios of 9-(l-Naphthyl)fluorenes Carrying Carbonyl Substituents at the 2-Position of the Naphthyl at 55°C... [Pg.43]

Close examination of the population ratios of the peri substituted compounds (Table 21) shows another point. That is, whereas the sc form of the methoxycarbonyl compound is less favored relative to that of the cyano compound when the peri substituent is methyl, the situation is reversed when the peri substituent is chlorine. Weak attractive interactions between a carbonyl moiety and a peri substituent bearing a lone pair of electrons are known in triptycene systems, and the methoxycarbonyl group is a stronger electron acceptor than cyano (148). This attractive interaction may be the cause for the seemingly anomalous populations. [Pg.59]

Kinetic Parameters for Rotation (ap — sc) and Population Ratios of 9-(2-Methoxy-l-methylethyl)triptycenes (114) in Chloroform- ... [Pg.66]

The barrier to rotation was 24.8 kcal/mol at 48°C, and the population ratio was 2.0 in chloroform-, which is the statistical value. The size of the peri substituent has an important effect on the barrier to rotation about the CH2—C(9) bond, because if a 1,4-dimethoxybenzeno bridge is introduced in place of the 1,4-dimethylbenzeno, the coalescence of the AB quartet due to the benzylic CH2 protons is observed at 167°C corresponding to a free energy of activation of 22 kcal/mol, which is too low for isolation of the atropisomers at room temperature. [Pg.68]

The torsional barrier of the amino group in thioamides is generally ca. 2 kcal/ mol higher than in the corresponding amides (26), and this trend is also found in the enamino thioketones (17,23 Table 2). The increased conjugative interaction in the thioamides is reflected in the Ct—C2 barriers, and the larger size of sulfur compared to oxygen affects the EIZ population ratio. [Pg.89]

The rotational population distributions were Boltzmann in nature, characterized by 7Ji = 640 35 K. This seems substantially lower than yet somewhat larger than the temperature associated with the translational degree of freedom. The lambda doublet species were statistically populated. The population ratio of i =l/t =0 was roughly 0.09, consistent with a vibrational temperature Ty— 1120 35K. The same rotational and spin-orbit distributions were obtained for molecules desorbed in t = 1 as for f = 0 levels. Finally, there was no dependence in the J-state distributions on desorption angle. [Pg.72]

The relative population ratio FJFi was slightly higher than expected from a 300 K thermal distribution (e.g. 2.1 vs 1.8). Of particular note, in comparison to a simple Boltzmann distribution, there was a substantial absence of population in the F2(J < S.S) levels from that expected based on a thermal (300 K) distribution. Approximately 1% of the desorbed molecules were vibrationally excited. [Pg.79]

Furthermore, the observed relative intensity of the 625 cm band to that of the 603 cm i band should be correctable with the AA/GA population ratio of the conformation equilibrium. The observed ratios depended slightly on the anion For the halides, it seems to increase in the order [BFJ [PF ]" == Cl < Br- < r [50]. [Pg.320]

Because the population ratio is determined by the appropriate Boltzmann expression where A is the energy difference between states and k is the... [Pg.102]

The population of nuclei in energy level E2 is slightly less than that in energy level Ei, which is a little more stable. Population ratio (Boltzmann distribution) calculations that can be conducted using equation (9.5) for T = 300 K and B0 = 5.3 T lead to R = 0.999 964 (where k = 8.314/6.022 x 10"23 J KT1). [Pg.131]

The population ratio N(E + AE)/N(E) can often be inferred from the intensities of spectroscopic peaks, for example, the rotational lines of a microwave spectrum. This seemingly... [Pg.28]

Calculate the population ratio at 25 °C of a and fi spin states for an isolated electron in a field of 10,000 G. Compare with Problem 8.6. [Pg.197]


See other pages where Population ratio is mentioned: [Pg.170]    [Pg.373]    [Pg.128]    [Pg.128]    [Pg.36]    [Pg.221]    [Pg.223]    [Pg.495]    [Pg.495]    [Pg.495]    [Pg.25]    [Pg.301]    [Pg.132]    [Pg.133]    [Pg.282]    [Pg.515]    [Pg.43]    [Pg.59]    [Pg.63]    [Pg.71]    [Pg.96]    [Pg.198]    [Pg.307]    [Pg.10]    [Pg.4]    [Pg.123]    [Pg.201]    [Pg.299]    [Pg.300]    [Pg.312]    [Pg.102]   
See also in sourсe #XX -- [ Pg.10 ]




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