State the meaning of random.
State the meaning of spontaneous.
State how Fig. 10.1 shows that radioactive decay is random.
On Fig. 10.1, draw the straight line that best fits the points.
A small sample of carbon-15 decays. The mass $M$ of carbon-15 in the sample falls with time $t$. Fig. 10.1 shows how the value of $\ln\left(\frac{M}{10^{-16}\,\text{g}}\right)$ varies with $t$.
Show that the decay constant $\lambda$ of carbon-15 is given by the magnitude of the gradient of your line in (b)(ii).
Use your line in (b)(ii) to find $\lambda$. Include a unit in your answer.
Use your answer in (b)(iv) to calculate the half-life of carbon-15.
The decay of carbon-15 may be written as $^{15}_{6}\text{C} \rightarrow ^{15}_{7}\text{N} + ^{0}_{-1}\beta + ^{0}_{0}\nu$. State and explain how the mass of the products of the decay compares with the mass of the carbon-15 nucleus.