CAIE A-Level Physics P5 Data Models and Graph Transformations

Practise linearising linear, power-law or exponential relationships by selecting graph axes, then linking each gradient or intercept to the model constant.

Exam points

linearise exponential or power relationships and use graph gradients to determine constants
choose calculated variables and logarithmic or linear plots appropriate to a physical model

[Maximum number: 1]

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 $=\lambda)$

B1

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P5.3-Data analysis models and graph transformations question 1