Radioactive Decay: Mean Life Time & Decay Constant

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The mean lifetime of a radioactive decay is defined as the average time a particle exists before decaying, mathematically represented as τ = 1/λ, where λ is the decay constant. This relationship can be proven by analyzing the decay process, where the number of remaining particles N(t) decreases over time, and the activity A(t) is the rate of decay, expressed as A(t) = -dN(t)/dt. The decay constant λ is directly proportional to the activity, linking it to the mean lifetime. By integrating the decay equations, one can derive the reciprocal relationship between mean lifetime and decay constant. Understanding this relationship is crucial for applications in nuclear physics and radiometric dating.
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How can we prove that the mean life time of a radioactive decay is reciprocal to the decay constant?
 
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roshan2004 said:
How can we prove that the mean life time of a radioactive decay is reciprocal to the decay constant?
What is the definition of 'mean lifetime' and how would one describe it mathematically?

Think about the survival time for a population of particles that decay, and how N(t) relates to A(t), where A(t) = dN(t)/dt.
 

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