Half Life of Barium

The nucleus of an atom consists of particles called nucleons, that are held together by a very strong nuclear force that has a very short range.    




Well some heavy atoms are just so big that this nuclear force can't keep all of the nucleons together forever, so eventually the nucleus loses some and becomes smaller.  




This is known as a nuclear decay, and it can be accompanied by a loss of energy  through the emission of one of three particles depending on the decay of the particle.

Alpha radiation:       A little chunk of nucleons consisting of four nucleons, (equivelant to a Helium atom) is emitted.
Beta radiation:        An is emitted electron
Gamma radiation:    A photon is emitted.

Now...if you have a chunk of such radiactive material, they will eventually all decay if you wait long enough, but they don't all decay at once. 

The probability of any one of them decaying within a given time period is constant.   It's given by the decay constant.

The probabilty of a decay to occur in the chunk of material, depends on the number of UNDECAYED atoms left.

Now there's an aweful lot of atoms in there, but if you could plot the number of UNDECAYED atoms in your sample as time progresses, the curve would have an decay exponentially like this.





If you  count the decays with a geiger counter.   You'd find that the number of decays in a 30 second interval would follow a similar time distribution.  

Let's call the number of decays in a 30 second time interval N.   
The number of decays in the first 30 second time interval that you measured N0.
And the time dependence of N is called N(t).




  Suppose you plotted the number of decays in a 30 second interval

 





Now you can't measure individual atoms, and you're not going to




The functional depends goes like this.