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A more precise definition of half-life is that each nucleus has a 50% chance of living for a time equal to one half-life \(t_{1/2}\). Thus, if \(N\) is reasonably large, half of the original nuclei decay in a time of one half-life.
The formula for mean life. The average life of any radioactive isotope has equaled the half-life of the substance divided by the natural log 2 which is exactly 0.693, and it’s equal to the number of τ which is represented in the exponential term e−t/τ in the decaying. It is called the time constant. Let ‘n’ be an active nucleus, the mean life is.
A radioactive nuclide has a high decay rate. What does this mean for its half-life and activity? Answer. Half-life is inversely related to decay rate, so the half-life is short. Activity depends on both the number of decaying particles and the decay rate, so the activity can be great or small.
The mean life of an element equals the half-life of the substance divided by the natural logarithm of 2 which is about 0.693. In fact, the mean life turns out to equal the number τ which appears in the exponential term e −t/τ involved in the description of decay or growth.
18 Μαρ 2022 · A nucleus has a probability of decaying within the next time interval, say $\delta t$, or not. Thanks to how statistics and probability work, if we have a large number of these nuclei, they will collectively exhibit a "mean lifetime" (i.e. we are able to obtain an average time it takes for one nucleus to decay).
Mean Lifetime for Particle Decay. The decay of particles is commonly expressed in terms of half-life, decay constant, or mean lifetime. The probability for decay can be expressed as a distribution function. where λ is called the decay constant.
It turns out that the mean life equals the half life divided by the natural logarithm of 2 (about 0.693). The mean life also turns out to exactly equal the number τ that appears in the exponential term e −t/τ involved with describing decay or growth, called the time constant .
