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Question:  How do they find the half-life of uranium238 and how 
do they know that radioactive decay is constant?
 c todnem

Answer:
Good question! I'll try to answer it. Radioactive isotopes
(like U238) can be isolated physically into rather pure forms
through a number of techniques, so let's assume we have a
chunk of pure U238. Now, every time a radioactive nucleau
decays, it gives off a chunk of nuclear matter which carries
a certain well-known  amount of energy characteristic of
the element (alpha particles, beta particles) or a photon
of high-energy radiation (a gamma ray). ThThe energy of these
particles can be measured uysing a device called a scintillation
counter. And the number of decays per unit time tells you how
fast the decay is happening. The half-life isthe amount of time
it takes for half of the original chunk of material takes to
radiaoactivelydecay.So, if you know how much matter you
start with and howmany decays happen per unit timew, you  can
figure out the half-life.
Now, how do we know that the rate of decay is constant? There are
sometheoretical reasons to believe that it should be, but most
importantly, for all radioactive substances which have been studied
(some of which decay rapidly, others slowly), careful experiments
have SHOWN this to bethe case. What's more, using thisassumption
to date old objects hasbeen proven to be accurate for athose artifacts
about which we know alittle about their creation date. So far
the vast majority of evidence points to the exponential decay of
nuclear materials (and consequently a single rate constant k;
N (t) = N0 exp(-kt). . - dr topper