Diane - I think you are wondering how a person can know the half-life of U238
or other very long-lived isotope.
Assuming that the nature of the nucleus is not time-dependent, the half-life
is easy to determine in the laboratory by measuring the rate of alpha particle
emission from a sample of the pure isotope. This can be done in a few hours
or minutes. The longer the half-life, the fewer alphas will be emitted per
second, from a sample contining a known amount of U238.
I hope this helps. Larry
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Lawrence H. Johnston 917 E. 8th st.
professor of physics, emeritus Moscow, Id 83843
University of Idaho (208) 882-2765
http://www.uidaho.edu/~johnston/ ===================