State what random means.
State what spontaneous means.
A small sample of carbon-15 decays. The mass $M$ of carbon-15 in the sample falls as time $t$ increases. Fig. 10.1 shows how the value of $\ln\left(M / 10^{-16}\,\text{g}\right)$ changes with $t$. State how Fig. 10.1 shows that radioactive decay is random.
On Fig. 10.1, draw the straight line of best fit.
A small sample of carbon-15 decays. The mass $M$ of carbon-15 in the sample falls as time $t$ increases. Fig. 10.1 shows how the value of $\ln\left(M / 10^{-16}\,\text{g}\right)$ changes with $t$.
Show that the decay constant $\lambda$ of carbon-15 is equal to 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 work out the half-life of carbon-15.
The decay of carbon-15 may be written as $^{15}_{6}\text{C} \rightarrow {}^{15}_{7}\text{N} + {}^{0}_{-1}\beta + {}^{0}_{0}\bar{\nu}$. State and explain how the mass of the decay products should compare with the mass of the carbon-15 nucleus.