A radioactive substance, with initial mass m₀ , has a half-life of h days. Then its initial decay rate is given by

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 m ₀=0+ c c = m ₀ m=-k t+ m₀ m m ₀ =- kt When t = h , m = 1 2 ~m ₀ ( 1 2 m₀ m₀ )=-k h aligned & 1 2 =- kh & 2= kh aligned k = 2 ~h ...(i) Initial decay rate, dm dt =- km ₀= - m ₀ ~h 2 ...[From (i)]