Atomic Theory Unit Half-Life

Introduction We have discussed the concepts associated with nuclear decay. You should be able to write nuclear equations for both alpha and beta decay processes. You should also know by now that alpha particles are weaker than beta particles which are in turn weaker than gamma radiation. alpha < beta < gamma

Now for Half-Life When a sample of a radioactive isotope undergoes nuclear decay, the individual atoms in the sample change at different times. They do NOT all change at the same time. Chemistry defines the time needed for 50% of the atoms in a radioactive sample to decay as the half-life of that isotope. Half-life is the time necessary for one-half of a sample to decay.

What does that mean? Suppose you know that the half-life of a particular isotope is 1 hour. That means that no matter how much of that isotope you have, 50% of it will decay in one hour. So, if you had 100 atoms of that isotope, about 50 of them would have decayed after one hour.

There is more… The question then becomes – what happens during the next hour? Do the other (remaining 50 ) atoms all decay in that next hour? The answer is “NO”. In the next hour, 50% of the atoms that remained after the first hour will decay. So at the end of the 2nd hour, you will have 25 atoms of the isotope remaining. The same thing will continue to occur each hour – half of what remains will decay.

Consider this graph

Calculations Involving Half-Life There are four different types of problems that involve the concept of half-life. We will look at a few examples. There are two questions that you have to keep in mind as you work through these problems. 1st – How many half-life cycles occur in the system described by the problem? 2nd – What happens to the mass each half-life cycle? Look at the next slide for the answers to these two questions…

Question #1: The way to determine the number of half-life cycles is to divide the total time given in the problem by the half-life (also given in a problem). You can use a pyramid – just like we did in density problems. cycles time t1/2

Question #2 What happens to the mass each half-life cycle? The answer to this question is always the same – the mass divides by two. So, if you are asked how much of an isotope will you have after three half-life cycles – all you have to do is divide the original mass by “2” – three times.

Example: You have 100 grams of a radioactive isotope. How much of this isotope will you have after 4 half-life cycles? As we saw in the previous slide, the mass gets divided by “2” each half-life cycle. Since there are four cycles in this problem, we will have to divide 4 different times.

Doing this gives the following results: Start 100 grams After Cycle #1 50 grams remaining After Cycle #2 25 grams remaining After Cycle #3 12.5 grams remaining After Cycle #4 6.25 grams remaining

The Pyramid cycles time t1/2 Use the pyramid to figure out how many half-life cycles occur. You must also remember that the mass divides by two every half-life cycle.