A certain radioactive nuclide has a half-life of 200.0 s. A sample containing just this one rad

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A certain radioactive nuclide has a half-life of 200.0 s. A...

A certain radioactive nuclide has a half-life of $200.0 \mathrm{~s}$. A sample containing just this one radioactive nuclide has an initial activity of $80,000.0 \mathrm{~s}^{-1}$. (a) What is the activity $600.0$ s later? (b) How many nuclei were there initially? (c) What is the probability per second that any one of the nuclei decays?

Key Concepts

Half-life

The half-life of a radioactive substance is the time required for half of the original number of radioactive nuclei to decay. It is a characteristic property of each radioactive nuclide and provides a measure of the rate at which a sample undergoes decay, independent of the initial amount present.

Exponential Decay

Exponential decay describes the process by which the quantity of radioactive nuclei decreases over time. This decay is governed by the equation N(t) = N0 exp(-?t), where N0 is the initial number of nuclei, ? is the decay constant, and t is time. The exponential nature also applies to related quantities such as activity, which decreases proportionally.

Activity of Radioactivity

Activity is the rate at which a radioactive substance decays, measured in disintegrations per unit time (for example, s?¹). It is directly proportional to the number of radioactive nuclei present and the probability per unit time that any particular nucleus will decay, and is described by the formula A = ?N.

Decay Constant

The decay constant is a parameter that quantifies the probability of decay of an individual radioactive nucleus per unit time. It is directly related to the half-life by the equation ? = ln(2) / t½. This constant is fundamental to describing the rate at which a sample of radioactive material decays.

Probability of Decay

The probability per unit time that a single radioactive nucleus will decay is given by the decay constant. This value reflects the intrinsic likelihood that any one nucleus will undergo a decay event in a given time interval and is independent of the number of nuclei in the sample.

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