On a single set of axes, two decay curves are plotted for equal initial samples of isotopes A and B. Both curves start at N0 undecayed nuclei at t=0.
• For isotope A, the curve passes through N=N0/2 at t=3.2h.
• For isotope B, the curve passes through N=N0/2 at t=5.6h.
Assume each isotope undergoes independent, single-mode radioactive decay. Use only information obtainable from the graph for all parts below.
(a) Identify which isotope, A or B, has the larger decay constant, and justify your answer qualitatively using the curves.
(b) Derive an expression for the ratio λA/λB and compute its numerical value from the given half-life information.
(c) At t=11.2h, determine the fraction N/N0 remaining for each isotope. Show all steps in your calculation.
(d) Discuss how an uncertainty of ±0.2h in reading each half-life from the graph would propagate into the value of λA/λB. Provide a qualitative assessment of the reliability of the ratio.