A radioactive sample intended for irradiation of a hospital...

A radioactive sample intended for irradiation of a hospital patient is prepared at a nearby laboratory. The sample has a half-
life of 83.61 h. What should its initial activity be if its activity is to be
$7.4 \times 10^{8}$ Bq when it is used to irradiate the patient 24 h later?

Key Concepts

Radioactivity and Activity

Radioactivity is the measure of the rate of decay of a radioactive substance, and activity refers to the number of disintegrations per second, measured in becquerels (Bq). The concept of activity is critical in fields such as medical physics, where knowing both the initial and desired activity levels is necessary for ensuring that a patient receives the correct dose during irradiation.

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a single nucleus will decay. It is closely related to the half-life via the formula ? = ln(2)/T?/?. Understanding the decay constant is crucial when using the exponential decay formula, as it directly affects the rate at which the radioactive sample loses its activity over time.

Half-life

The half-life of a radioactive substance is the time required for half of the material to decay. It is a characteristic property of each radionuclide. In the context of exponential decay, the half-life T?/? is used to relate the decay constant and time, specifically through the relationship T?/? = ln(2)/?. This concept allows one to calculate the remaining activity or determine the necessary initial activity for a required activity at a later time.

Exponential Decay

Exponential decay refers to the process by which the quantity of a radioactive substance decreases over time at a rate proportional to its current amount. The decay is described by the equation A = A?e^(??t), where A? is the initial activity, A is the activity at time t, and ? is the decay constant. This law is fundamental for understanding how radioactive samples behave over time.

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