Radioactive decay is described by the statement that the instantaneous rate at which…
CHEMISTRY · Subjective · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear
Problem
Radioactive decay is described by the statement that the instantaneous rate at which nuclei disintegrate is directly proportional to the number of undecayed nuclei present at that instant.
(i) Write the differential equation that expresses this statement for the number of undecayed nuclei N(t) at time t.
(ii) Solve the differential equation of part (i) to obtain the general expression for N(t) in terms of the initial number N0 and the decay constant.
(iii) From the expression obtained in part (ii), derive a formula connecting the half-life T1/2 of the isotope with its decay constant.
(iv) Explain qualitatively how the numerical value of the decay constant influences the steepness of the decay curve and the practical lifetime of the isotope.