Isotope P is a pure β-emitter that decays directly to a stable daughter isotope D
CHEMISTRY · Multi-part · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear
Problem
Isotope P is a pure β-emitter that decays directly to a stable daughter isotope D. A chemist isolates a 3.0 mg sample of P at time t=0. The half-life of P is 12 h. No daughter nuclei are present initially.
(a) Derive an expression for the mass of P remaining at an arbitrary time t in terms of the given half-life and the initial mass m0.
(b) Using your result from part (a), compute the mass of P that remains after 36 h.
(c) Determine the mass of daughter nuclei D that have been produced after 36 h. Neglect any mass–energy conversion effects and assume the mass of a parent nucleus equals the mass of a daughter nucleus for the purpose of this calculation.
(d) Discuss, in qualitative terms, why the actual total mass of the sample after 36 h is slightly less than the sum of the masses you calculated in parts (b) and (c). Relate your discussion to fundamental principles of nuclear reactions.