A pure sample of a radioactive isotope is studied in the laboratory.
(i) Sketch qualitatively the expected variation of the number of undecayed nuclei N with time t.
(ii) On a separate set of axes, sketch the graph of lnN versus t for the same sample.
(iii) Explain, with reference to your sketches, why the half-life of the isotope remains constant even though the number of undecayed nuclei decreases with time.
(iv) Two different isotopes P and Q obey the same decay law but have decay constants λP>λQ. Without doing any calculations, state which of the two curves in each sketch will be steeper and justify your answer.
a. (i) Qualitative sketch of N versus t
b. (ii) Qualitative sketch of lnN versus t
c. (iii) Explanation of constancy of half-life
d. (iv) Identification of steeper curve for isotopes P and Q with justification