The time required for half of a radioactive sample to decay is called?

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Multiple Choice

The time required for half of a radioactive sample to decay is called?

Explanation:
Half-life is the time required for half of a radioactive sample to decay. In exponential decay, the number of undecayed nuclei N(t) follows N(t) = N0 e^{-λ t}, where λ is the decay constant, the probability per unit time that a given nucleus will decay. To find the half-life, set N(t1/2) = N0/2 and solve: N0/2 = N0 e^{-λ t1/2} ⇒ t1/2 = ln 2 / λ. This shows the half-life is a constant for a given nuclide and does not depend on how much material you start with. The decay constant is a rate parameter, not a time. Activity A = λN is the number of decays per unit time and changes as the sample decays, but it does not describe the time required for half the material to decay. The term isotopic half-life is essentially the same concept, but the standard term is simply half-life.

Half-life is the time required for half of a radioactive sample to decay. In exponential decay, the number of undecayed nuclei N(t) follows N(t) = N0 e^{-λ t}, where λ is the decay constant, the probability per unit time that a given nucleus will decay. To find the half-life, set N(t1/2) = N0/2 and solve: N0/2 = N0 e^{-λ t1/2} ⇒ t1/2 = ln 2 / λ. This shows the half-life is a constant for a given nuclide and does not depend on how much material you start with. The decay constant is a rate parameter, not a time. Activity A = λN is the number of decays per unit time and changes as the sample decays, but it does not describe the time required for half the material to decay. The term isotopic half-life is essentially the same concept, but the standard term is simply half-life.

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