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8. What is the half-life of an element?
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The half-life of an element (more precisely, of a radioactive isotope) is the time required for half of the nuclei in a sample to decay.
For a sample with initial number of radioactive nuclei N0, the number remaining after time t is
N(t) = N0 e^(−λt),
where λ is the decay constant. The half-life t1/2 is related to λ by
t1/2 = ln 2 / λ ≈ 0.693 / λ.
The half-life is a statistical property of the isotope and does not depend on the initial amount of material (though very short-lived isotopes can be affected by extreme conditions in rare cases).
For a sample with initial number of radioactive nuclei N0, the number remaining after time t is
N(t) = N0 e^(−λt),
where λ is the decay constant. The half-life t1/2 is related to λ by
t1/2 = ln 2 / λ ≈ 0.693 / λ.
The half-life is a statistical property of the isotope and does not depend on the initial amount of material (though very short-lived isotopes can be affected by extreme conditions in rare cases).
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