Now when it comes to 1st order and half life, first realize that all radioactive processes follow a first order rate law. So for reactions with first order we use the following equation and that is half life equals ln2K. Now if you plug in ln2 in your calculator, you're going to get 0.693 and it'll still be over K. OK, so just be aware of that. You may see on your formula sheet, instead of ln2, you may see 0.693. That's where it comes from.
Now here we're going to say ln2 is our constant. In this case we're going to say K is our rate constant. And here we'd say since it's dealing with first order, it D be units of time. Inverse T of course is time. When it's T half it's half light. Now what can we say about this half life equation and concentration? Well, if we take a look, half life equals ln2K we don't see initial concentration of our reactant anywhere.
So that means half life does not depend on the initial concentration of our reactant and as a result of this, it's going to be constant throughout the whole reaction. So that means half five is just going to stay flat because K is going to be a number that's not going to change and ln2 is always the same number as well. So half life is going to stay consistent throughout the whole reaction.
Now you remember if we do a plot, it's of Y versus X Y here would be half fly. So that's why it's on the Y axis and X here is T for time, that's why it's on over here on the X axis. So keep these little facts in the back of your mind when dealing with half life and 1st order rate law equations.