A radio-active substance has a half-life of h days, then its initial decay rate is given by (where radio-active substance has initial mass m ₀ ).

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