What is half-life?

• A. The average time it takes for half of existing radioactive isotopes to decay
• B. The energy released per decay
• C. The total lifetime of a nucleus
• D. The time to double the number of nuclei

Answer: (A)

Half-life is the time required for half of the unstable nuclei in a sample to decay. It is a characteristic constant for a given isotope and sets the exponential decay rate: after one half-life, roughly half remains; after two, a quarter; and so on. This time scale is independent of how much material you started with and is not about how much energy is released per decay or the total lifetime of a nucleus. The energy per decay and the total time a nucleus exists are separate quantities. A quick way to relate it is that the half-life T1/2 connects to the decay constant λ via T1/2 = ln 2 / λ. For example, with a 5-hour half-life, starting from 1000 nuclei leaves about 500 after 5 hours, about 250 after 10 hours, etc.