An experimenter records the number of undecayed nuclei N of a radioactive sample at equal time intervals. The observations are:
Time t (min): 0, 2, 4, 6, 8
Number of nuclei N: 8000, 5657, 4000, 2828, 2000
(i) Convert the data so that log10N is tabulated against t and draw the graph on a semi-logarithmic sheet.
(ii) Using the best-fit straight line, determine the numerical value of the slope. Explain how this slope is related to the decay constant.
(iii) Hence calculate the decay constant λ and the half-life of the sample.
(iv) Using your graph, estimate the time at which the number of undecayed nuclei will fall to 500.
(v) Comment briefly on how the appearance of the curve would differ if an ordinary linear graph of N versus t were drawn instead of the semi-log plot.