Statistical nature of radioactive decay

Even if the experimental design and execution are perfect so that the determinant error is eliminated in experiments involving radioactivity there is always a random error due to the statistical nature of radioactive decay. Each radioactive atom has a certain probability of decay within any one time interval. Consequently, since this probability allows unlikely processes to occur occasionally and likely processes not to occur in any particular time interval, the number of decays may be more or less than the number in another similar... 

The statistical nature of radioactive decay also leads to an uneven distribution of decays in time which is important when handling dead-time corrections and discussing required system time resolution. Let us first assume that a decay has occurred at time t = 0. What is then the differential probability that the next decay will take place within a short time interval, dr, after a time interval t has passed Two independ t processes must then occur in series. No decay may take place within the time interval from 0 to r, probability P 0),... 

On account of the statistical nature of radioactive decay it is advisable to perform each measurement three times. 

As a measure for the mixture homogeneity the relative standard deviation of the measured count rates can be used. It is important to subtract the variations due to the statistical nature of radioactive decay, which would otherwise contribute to the measured variance. It has to be noted that the determination of homogeneity is not unambiguous. The variations in tracer concentration of samples depend on the sample size and on the microstructure of the material. 

While it is true to say that all scientific measurements are estimates of some unattainable true measurement, this is particularly true of radioactivity measurements because of the statistical nature of radioactive decay. Consider a collection of unstable atoms. We can be certain that all wiU eventually decay. We can expect that at any point in time the rate of decay will be that given by Equation (5.1). However, if we take any particular atom we can never know exactly when it will decay. It follows that we can never know exactly how many atoms will decay within our measurement period. Our measurement can, therefore, only be an estimate of the expected decay rate. If we were to make further measurements, these would provide more, slightly different, estimates. This fundamental uncertainty in the quantity we wish to measure, the decay rate, underlies ah radioactivity measurements and is in addition to the usual uncertainties (random and systematic) imposed by the measurement process itself. 

For a proper approach to any radiometric problem, both familiarity with techniques and understanding of the nature of radioactive decay with related statistical aspects are required. 

Standard deviation is one of the parameter to characterise image quality. It defines the presence of noise component in image. Which is due to many reasons, e.g., random nature of radioactive decay, scattered gamma photons, low counting statistics, as well as genertaed by image reconstruction, analysis, and also attenuation correction techniques. 

Statistical nature of some processes, e.g., radioactive decay. There is a probability that an atom of a radioactive isotope will decay in the next 10 s, and this is as much information as one can report on this matter. The probability can be calculated, but it is still a probability, never a certainty. 

In principle, the statistics of radioactive decay are binomial in nature. If we were to toss a handful of coins onto a table and then examine the arrangement, we would find coins in one of two dispositions - heads up or tails up. Similarly, if we could prepare a radioactive source and, during a particular period of time, monitor each individual... 

Radioactive decay is a statistical process, there being nothing in any nucleus that allows us to predict when it will decay. The probability of decay in a given time interval is the only thing that can be determined, and this appears to be entirely constant in time and (except in the case of electron capture) unaffected by temperature, pressure or the chemical state of an atom. The probability is normally expressed as a half-life, the time taken for half of a sample to decay. Half-lives can vary from a fraction of a second to billions of years. Some naturally occurring radioactive elements on Earth have very long half-lives and are effectively left over from the synthesis of the elements before... 

Because of the random nature of the radioactive decay, the laws of statistics also have to be applied for the interpretation of radioactivity measurements. 

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