Decay fraction

By fitting the calculated decay fractions to the measured ones, the values of (A - AEm l)/AEn are readily determined. 

Until now, most studies of dissociation dynamics of metastable cluster ions have been made using a double-focusing mass spectrometry method (Lifshitz et al. 1990 Lifshitz and Louage 1989, 1990 Stace 1986). As discussed herein, the novel technique of reflectron time-of-flight mass spectrometry is a valuable alternative approach to more standard methods. With carefully designed experiments, it is possible to derive both kinetic energy releases and decay fractions for... 

The general procedure for measuring the decay fractions is given in subsection... 

The decay fractions, D = /d/(/d + /p) where /d and 7P are the daughter and parent ion intensities, respectively, can be measured with high precision by integrating the parent and daughter ion peaks. 

A typical hard reflection time-of-flight mass spectrum of ammonia clusters is shown in Figure 6-8(a). When the reflecting voltage is reduced, only the daughter ions are reflected, as shown in Figure 6-8(b). To precisely measure the metastable decay fractions, the soft reflection mode is used for a number of reasons discussed elsewhere (Wei et al. 1990a,b). 

Using eqs. (6-3) to (6-6), it is possible to determine relative bond energies for the clusters from measurements of the decay fractions. The deduced values of... 

Figure 6-10. A plot of measured decay fractions as a function of cluster size, n ( ) measured points, (-------) eq. (6-1).

Figure 6-12. A plot of binding energies as a function of cluster size n ( ) literature values (Keesee and Castleman 1986) (A) Klots model, decay fractions (x) Klots model, KER ( + ) Engelking s model, KER.

Figure 6-12 displays the binding energies of (NH3) H+, n = 4-17, as a function of cluster size n (labeled as x ) using the measured KER and y = 24.5, C = 6(n — 1), and compares the data with prior measurements based on high pressure mass spectrometry and values deduced from decay fractions. 

The salt used in this experiment is potassium chloride (KC1). Potassium-40 is a naturally-occurring isotope of potassium (abundance = 0.0117%) whose half life is 1.28 x 109 years. It emits a gamma ray at 1.461 MeV with a decay fraction of 10.7%, in addition to beta particles with a decay fraction of 89.3%. The decay scheme for 40K is given in Fig. 3.1. A tared container (see Experiment 2) is filled with solid KC1, closed, weighed, and counted. 

The net count rate at a given mass, Rm, is related to the self-absorption factor at that mass, fm, in terms of the activity, A, gamma-ray decay fraction, d, and counting efficiency at zero self-absorption, e0, by Equation 3.2 ... 

Calculate the ratio of the net count rate to the disintegration rate of K gamma rays in the sample, based on the half life, gamma-ray decay fraction, ratio of 40K to potassium mass, and K/KC1 ratio of 39.1/74.6. Calculate the self-absorption factor with Eq. 3.1. Calculate the counting efficiency at zero self-absorption with Eq. 3.2 and record in Data Table 3.3. 

The efficiency of the detection system is based on both detector and sample parameters. Detector parameters include the intrinsic detector efficiency, the geometric relation of detector to sample, scattering by the sample support and nearby material, and attenuation between the sample and the detector. Sample parameters include material stopping power based on composition, mass, diameter and thickness type and amount of sample cover and backing and radiation type, energy, decay fraction, and decay rate. 

Rm = net beta particle counts per s of 131I at the time the sample was counted (note that the decay fraction for beta particles is 1.00)... 

D89Sr = Decay fraction of89 Sr Y = chemical yield of strontium eSr 90 = counting efficiency of 90Sr eY 90 = counting efficiency of 90Y Sr 89 = counting efficiency of 89Sr... 

In the above model the mobile or slow decay fraction, fp, is state B, and the less mobile fraction(l-fpi) is the combined bound state A. The intercept of a free induction decay with the y- axis is proportional to the paramagnetic susceptibility of the specimen, and hence the number of protons in the specimen is proportional to inverse temperature. Since the less mobile fraction has decayed before the instrument has recovered from its 90° pulse (in < 20 y sec) the magnitude of the intercept Ip, at zero time for the free induction decay reflects the number of protons in the mobile fraction only. Thus, as the temperature, T is varied, the product Ip,T, is proportional only to the mobile water molecules. 

Figure 10.18 Plot of decay fraction D/(D + P) [Daughter/fDaughter + Parent)] of (NHjf CHjCNlH as a function of n. Open squares are the experimental results, while the solid lines are calculated curves based on equation (10.59). The assumed functional forms for the heat capacity are C = 6(n - 1) + 8 (upper line) and C = 6(rr - 1) (lower line). Taken with permission from Tzeng et al. (1991).

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