How is decay rate related to the half-life of a radioisotope?
The decay rate determines the half life of a radioisotope.
The half life is the time required for half of an existing isotope to decay. The faster the decay rate the shorter the half life will be. This is because the faster the decay rate the sooner half of the isotope will be gone. The slower the decay rate the longer the half life will be. Uranium 238 is much more stable than Uranium 235 so it has both a slower decay rate and a longer half life.
The decay rate is inversely proportional to the half-life.
The relation between the rate constant
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This is an inverse proportionality.
The decay rate decreases at the half-life increases, and vice versa.