Explain the Half-Life

The decay of a nucleus is a random event.  It is not possible to predict which nucleus will decay and when.  Even though over a period of time, the decay rate is constant that permits us to predict when a given fraction of the sample has decayed.

The half-life is the amount of time it takes for half of a chunk of radioactive isotope to go through radioactive decay.  It is generally represented by the symbol t_½ .

The half-life of germanium-69 is 36 hours.  If we begin with n atoms of ⁶⁹₃₂Ge, then at the end of 36 hours we will comprise n/2 (half) of the atoms of ⁶⁹₃₂Ge left.  The rest of the atoms will have altered into another element or isotope. At the end of the next 36 hours (that is 72 hours from the starting point) there will be n/4 atoms of ⁶⁹₃₂Ge left.  After other 36 hours have passed (108 hours from the beginning) there will be n/8 ⁶⁹₃₂Ge atoms.  Observe the trend?  After every half-life we have half of the preceding amount.