Mean life

For fluorescent compounds and for times in die range of a tenth of a nanosecond to a hundred microseconds, two very successftd teclmiques have been used. One is die phase-shift teclmique. In this method the fluorescence is excited by light whose intensity is modulated sinusoidally at a frequency / chosen so its period is not too different from die expected lifetime. The fluorescent light is then also modulated at the same frequency but with a time delay. If the fluorescence decays exponentially, its phase is shifted by an angle A([) which is related to the mean life, i, of the excited state. The relationship is... 

That is, ia this case there is only a 36.8% chance of surviving the mean life. If the distribution were other than exponential, the chance of survival would change. Since the mean life is not associated with constant reUabiUty, the expected life should not be the only indicator of reUabiUty, particularly when comparing products. 

Point Estimation. The estimator for the mean life parameter 0 is given by... 

From equation 8 it was shown that the chance of surviving the mean life was 36.8% for the exponential distribution. However, this fact must be used with some degree of rationaHty in appHcations. For example, in the above situation the longest surviving MPU that was observed survived for 291.9 hours. The failure rate beyond this time is not known. What was observed was only a failure rate of A = 1.732 x lO " failures per hour over approximately 292 hours of operation. In order to make predictions beyond this time, it must be assumed that the failure rate does not increase because of wearout and... 

Since fatigue cracks often start at a random surface imperfection, considerable scatter occurs in fatigue data, increasing with the increasing lifetime wherever crack initiation occupies most of the fatigue life of a specimen. When a line of the best fit is drawn from the available data points on an S-N curve, this represents the mean life expected at any given stress level or the stress that would cause, say, 50% of the product failures in a given number of cycles. 

Although the general circulation patterns are fairly well known, it is difficult to quantify the rates of the various flows. Abyssal circulation is generally quite slow and variable on short time scales. The calculation of the rate of formation of abyssal water is also fraught with uncertainty. Probably the most promising means of assigning the time dimension to oceanic processes is through the study of the distribution of radioactive chemical tracers. Difficulties associated with the interpretation of radioactive tracer distributions lie both in the models used, nonconservative interactions, and the difference between the time scale of the physical transport phenomenon and the mean life of the tracer. 

The decay constant, X, defines the probability that a particular atom will decay within a given time (X = In 2/t1/2). The half-life (t1/2) describes a time interval after which N = NJ2. The observed counting rate or activity (A) is equal to XN. Another way to describe radioactive decay is in terms of the mean life (t) of a... 

Table 8-7 as well as the efficiency at the mean life. The mean is the length of time the lamps are expected to bum. 

Mean Life, Attachment, Recombination and Plateout. The approximate mean life (T) of Po-218 in ion form can be represented as ( X + an + N + po) where X is the decay constant for Po-218, a is the recombination coefficient for Po-218 and ordinary ions of negative charge in the atmosphere, n is the concentration of small negative ions, 8 is the attachment coefficient, N is the number of condensation... 

In this type of thermometry, long mean-life radioactive nuclei are used. The latter perform a J8 decay into an excited state which emits y to return to the fundamental state... 

As a main feature, the usage of a conducting matrix can be expected to help to decrease the resistance and to increase the mean life of the generated electrons. Also, a porous conducting electrode enables a more intimate contact between the electrode and the semiconductor. Despite the prelimi-... 

The method assumes that the average cosmic ray flux has been constant over the mean-life of 81Kr (t81 + 3.07 x 105y) and over the overall exposure time of the sample cosmic rays. Furthermore, it is assumed that the exposure geometry has remained fixed over the period of irradiation, but no other assumptions are made regarding shielding. 

Another isotopic anomaly, discovered in Allende inclusions, concerns magnesium, for which an intrinsically low abundance in these samples makes its isotope ratios sensitive to small effects. Certain of the inclusions show a correlation between 26Mg and 27 Al, indicating an origin of excess 26Mg from radioactive decay of 26 A1 (mean life 1 Myr), the existence of which had previously been postulated as a heat source for meteorite parent bodies (Fig. 3.32). Other short-lived activites that seem to have been alive in the early Solar System are 10Be (mean life 2.2 Myr) from a correlation of 10B with 9Be, and 41Ca (mean life 0.15 Myr) from a correlation of... 

From the abundances of the radioactive nuclei 10Be (mean life 2.2 Myr) and 26A1 (mean life 1.0 Myr), one also has an idea of the timescale for escape, which seems to be of the order of 107 yr and perhaps an order of magnitude longer than the time to pass through A at an average density of one atom (2 x 10-24 gm) cm-3 in the Galactic plane. 

Fig. 10.6. Log-log plot of against mean life (Gyr). Data from Table 10.2 and Wasserburg, Busso and Gallino (1996), with estimated error bars.

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