(Comparative Decay Problem)
Equal numbers of atoms of two different radioactive isotopes A and B are placed in separate but identical detectors at time t=0. The half-life of isotope A is known to be 12 h, whereas the half-life of isotope B is unknown. After 36 h the activity (rate of decay) of isotope A is found to be four times the activity of isotope B.
(i) Express the activities of isotopes A and B at t=36 h as fractions of their respective initial activities.
(ii) Using the result of part (i), form an equation relating the decay constant of isotope B to that of isotope A.
(iii) Hence calculate the half-life of isotope B, correct to two significant figures.