Half-Life Calculation: How Do Physicists Measure Isotopes?

[Danscall]

Hi there,

Someone asked me this earlier when we were talking about radioisotope dating. How do physicists determine the half lives of isotopes when said half life stretches into the millions of years?

Random question I know :P

-Dan

 

[phyzguy]

It's not hard to do this. The reason we can do this is that atoms are so small that a macroscopic sample of some isotope contains a huge number of them. So if I have a gram of U-238, for example, with a half-life of 4.5 billion years, I would need to wait 4.5 billion years for half of it to decay. But a gram of U-238 contains (6.02x10^23)/238 ~ 10^21 atoms. So even though the probability of a single nucleus decaying is quite small, in a gram about 12,000 nuclei will decay every second. This can be easily measured, and from the number that decay every second, we can calculate the half-life. The number that decay every second is called the "activity". Try reading these:

http://en.wikipedia.org/wiki/Radioactive_decay
http://en.wikipedia.org/wiki/Half-life

 

[Astronuc]

Hi there,

Someone asked me this earlier when we were talking about radioisotope dating. How do physicists determine the half lives of isotopes when said half life stretches into the millions of years?

Random question I know :P

-Dan

One can measure an activity and from that a decay constant. One can also measure the daughter isotopes and from that determine a rough estimate of where in the decay time the particular radionuclides are. However, this requires an assumption about the original composition.