Successive Decay Nuclide Concentration — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Successive Decay Nuclide Concentration This formula describes the concentration of a daughter nuclide ( N 2 ) formed from a parent nuclide ( N 1 ) undergoing radioactive decay, assuming the initial concentration of the daughter nuclide is zero. Start with the coupled differential equations for successive decay: dN 1 dt = - 1 N 1 and dN 2 dt = 1 N 1 - 2 N 2. Solve the first equation to find N 1(t) = N 1(0) e - 1 t . Substitute N 1(t) into the second equation and solve the resulting first-order linear differential equation for N 2(t) . The final solution yields the given expression for N 2(t) . 1 2 t 0 N 2(0) = 0 Assuming the decay follows simple exponential decay when two steps are involved. Forgetting the initial condition N 2(0)=0 , which is crucial for the derived formula. Confusing the decay constants ( ) with the half-lives ( T 1/2 ), forgetting the relationship = 2 T 1/2 .