Question: If there are N0 radioactive nuclei at time t = 0, the number that decay in some time interval dt at time t is dN

If there are N0 radioactive nuclei at time t = 0, the number that decay in some time interval dt at time t is dN = λN₀e^{– λt} dt. If we multiply this number by the lifetime t of these nuclei, sum over all the possible lifetimes from t = 0 to t = ∞, and divide by the total number of nuclei, we get the mean lifetime t:

laN =1 the dt No

Show that t = 1/λ.

laN =1 the dt No

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