Radioactivity is not a periodic phenomenon, when a nucleus emits radiation, nothing is repeated cyclicly.
Half-life is what we call the time that half the radioactive atoms in a sample take to transmute: it is the time necessary for the No of initial atoms to become No/2. In this time No/2 different atoms are formed, transmuted from the initial ones.

Given the exponential form of the decay, the sample can take a long time to become inactive. This, together with the fact that the decay processes cannot be accelerated, is one of the dangers of radioactivity. 

If we have a million radioactive atoms and the half life is one year, they will take a year to decrease to   500.000.
But at the end of this year there will still be  250.000, and another year later  125.000. Less and less atoms decay in the same time period.

No of initial atoms T1/2 to become No /2. 

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