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Carbon-15 $\left({ }_{6}^{15} \mathrm{C}\right)$ is an isotope of carbon that undergoes radioactive decay to nitrogen-15 $\left({ }_{7}^{15} \mathrm{~N}\right)$ , which is a stable isotope of nitrogen.

Radioactive decay is both a random and a spontaneous process.

A small sample of carbon-15 decays. The mass M of carbon-15 in the sample decreases with time t.

Fig. 10.1 shows the variation with t of the value of $\ln \left(M / 10^{-16} \mathrm{~g}\right)$ .

Fig. 10.1

Show that the decay constant $\lambda$ of carbon-15 is given by the magnitude of the gradient of your line in (b)(ii).

$M=M_{0} \exp (-\lambda t)$

so $\ln M=\ln M_{0}-\lambda t$ so gradient $=-\lambda($ and magnitude of gradient $=\lambda)$

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CAIE A-Level Physics A2 P5.3 Data Analysis Models and Graph Transformations Topic Practice

Question 1