A sample of copper-64 gives a reading of 88 counts per...

A sample of copper-64 gives a reading of 88 counts per second on a radiation counter. After $9.5 \mathrm{~h}$, the sample gives a reading of 53 counts per second. What is the half-life (in hours) of copper-64?

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Key Concepts

Decay Constant

The decay constant, represented by ?, is a parameter that quantifies the rate of radioactive decay. There is a direct relationship between the decay constant and the half-life, given by the formula t1/2 = ln2/?, establishing a fundamental connection between the rate of decay and the time it takes for the sample to decrease to half its initial activity.

Radioactive Activity Measurement

Activity in radioactivity refers to the number of decays per unit time, typically measured in counts per second. This measurement is directly proportional to the number of undecayed nuclei present, allowing changes in activity over time to be used to determine properties like the half-life.

Exponential Decay

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value. In the context of radioactive decay, this means that the number of radioactive atoms decays exponentially over time, allowing the use of equations such as N = N0 exp(-?t) to model the behavior of a decaying sample.

Half-life

The half-life is the amount of time required for half of a sample of a radioactive substance to decay. It is a characteristic property of a radioactive isotope and provides a straightforward measure of how quickly the substance loses its activity.

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