How do we know the half life of certain isotopes?

Question

For instance, carbon-14 has an approximate half life of 5730 years, but there is no way of observing decay in this isotope for that length of time (as far as I can see, but I've only studied science to GCSE level so far). Just interested to find out.

Answer 1

the half life is *defined* as the time required for half of the sample to decay. it quantifies the rate of decay, since the rate has a known mathematical form (exponential decay). but there is no need to actually wait for half the sample to decay... as long as you can count *some* decay events, you can calculate the halflife. that is to say, it's not strictly a time that's actually being measured, but a rate of decay.

some isotopes that have half lives counted in billions of years... nevertheless a typical sample has so many atoms in it (well over 10^20) that some will decay if you watch it for long enough, allowing calculation of the half life.

to put it another way, you could define a "0.01% life" parameter, that would be the time taken for 0.01% of the original sample to decay. that would correspond to a time much shorter time than the half life, but would be determined by making exactly the same measurements.

Answer 2

There is no need to wait an entire half-life in order to measure the rate of decay, just like there is no need to drive for an entire hour to measure your speed in miles per hour.

Answer 3

The half-life refers to the decrease in its radioactivity. There are instruments that can measure a given radioactive elements radioactivity. By observing the amount of decrease in its radioactivity over time, a calculation can be used to figure out how long before half of its radioactivity is gone. You bring up a valid point in that knowing that radioactivity has only been discovered for a little over one hundred years, how can you accurately extrapolate out for this length of time? In reality that is a problem due to statistical reasons. The truth is that radioactive deacay for a single atom is fairly unpredictable. A single atom of Carbon 14 may decay at any time from one minute up to tens of thousands of years. But if you have billions or more of the atom, you can predict an average of when they will deacy. For Carbon 14 the average is that half of the atoms will decay in about 5700 years.