importance of half-life of radioactive element?

Answer 1

radioactivity comes from the inbalance of electrons to protons. The extra electrons shoot off. When the balance is more equal, it has expired it's "life" as radioactive.

The shorter the half-life, the more dangerous in the short term. But it only needs to be contained for a short while.
The longer the half life, the longer it can contaminate.

Answer 2

There are an extremely large number of atoms in a small amount of a substance. Any of those atoms can decay in any given instant. It is not predictable.

Therefore, all you can do is find a statistical measure to indicate the rate of decay. It turns out that it decays at an exponential rate. This is best characterized by a "half-life". With an exponential rate of decay, the time for half of the material to decay is the same as the next quarter, and the next eighth. In other words, the material becomes half at a constant rate.

Answer 3

the decay rate tells you how radioactive it is in a rough way. short half life radioactivity is high, long half life and the radioactivity is low. (this does not indicate the type of particles emitted), just the relative rate of decay. It also gives you a way to guess how long the decay has been going on. Useful to geologists for carbon dating fossils.