The halflife is the amount of time it takes for half of the atoms in a sample to decay. The halflife for a given isotope is always the same ; it doesn't depend on how many atoms you have or on how long they've been sitting around.
For example, the applet will tell you that the halflife of beryllium 11 is 13.81 seconds. Let's say
you start with, oh, 16 grams of 11Be. Wait 13.81 seconds, and you'll have 8 grams left;
the rest will have decayed to boron 11. Another 13.81 seconds go by, and you're left with 4 grams of
11Be; 13.81 seconds more, and you have 2 grams...you get the idea.
Hmmm...so a lot of decays happen really fast when there are lots of atoms, and then things slow down
when there aren't so many. The halflife is always the same, but the half gets smaller and smaller.
That's exactly right. Here's another applet that illustrates radioactive decay in action.
Notice how the decays are fast and furious at the beginning and slow down over time; you can see this both from the color changes in the top window and from the graph.
You'll also notice that the pattern of atoms in the top picture is random-looking, and different each
time you run the applet, but the graph below always has the same shape. It's impossible to predict when
a specific atom is going to decay, but you can predict the number of atoms that will decay
in a certain time period.