Figure 42-19 shows the decay of parents in a radioactive...

Figure $42-19$ shows the decay of parents in a radioactive sample. The axes are scaled by $N_{s}=2.00 \times 10^{6}$ and $t_{s}=10.0 \mathrm{s}$ .
What is the activity of the sample at $t=27.0 \mathrm{s?}$

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Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process occurs spontaneously according to probabilistic rules and results in an exponential decrease in the number of undecayed nuclei over time.

Exponential Decay Law

The exponential decay law mathematically describes how the number of radioactive nuclei decreases with time. It is given by the formula N(t) = N0 e^(-?t), where N0 is the initial number of nuclei, ? is the decay constant, and t is time. This law underpins predictions about the behavior of radioactive samples.

Activity

Activity is a measure of the rate of decay in a radioactive sample, defined as the number of disintegrations per unit time. It is commonly expressed in becquerels (Bq) or counts per second (cps), and is proportional to both the number of undecayed nuclei and the decay constant of the material.

Graphical Scaling

Graphical scaling involves interpreting data from plots where the axes are marked in scaled units. Understanding the scale factors allows one to convert graph units back into standard units (such as time and number of decays), which is essential for applying mathematical models like the exponential decay law to real-world measurements.

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