A radio active substance has half-life of h days, then its initial decay rate is given by Note that at t =0, M = m _ o

Step-by-step solution

Let M be the mass of substance at time t . Then, aligned & dM dt =- kM , where k 0 & dM M =- kdt aligned Integrating on both sides, we get M=-k t+c When t =0, M = m ₀ array ll & m ₀=0+c & c = m ₀ & M =- kt + m ₀ & M ~m ₀ =- kt array gathered When t = h , M = 1 2 ~m ₀ ( 1 2 ~m ₀ ~m ₀ )=- kh 1 2 =- kh 2= kh k = 2 ~h ...(i) Initial decay rate, dM dt =- km ~m ₀ = - m ₀ ~h 2...[From(i)] gathered