Question

Consider the chain decay in radioactivity A +(λ_A)→ B + (λ_B)→ C,

where λ_A and λ_B are the disintegration constants. The equations for the radioactive decays are: 

(dN_A(t))/dt = −λ_ANA(t), and (dN_B(t))/dt = −λ₂N_B(t) + λ_AN_A(t) 

where N_A(t) and N_B(t) are the number of atoms of A and B at time t, with the initial conditions N_A(0) = N⁰_A; N_B(0) = 0. Apply Laplace transform to obtain N_A(t) and N_B(t), the number of atoms of A and B as a function of time t, in terms of N⁰_A, λ_A and λ_B.

Answer 1

dN_A(t)/dt = −λ_AN_A(t)  (1)