The rate of decay of mass of a certain substance at time 't' is proportional to the mass at that instant. The time during which the original mass of m₀ gm. will be left to m₁ gm . is (K is constant of proportionality)

Step-by-step solution

Given dm dt m dm dt =- Km dm m = - Kdt m =- Kt + c When t =0, ~m = m ₀ m ₀=0+ c c = m ₀ m =- Kt + m ₀ ( m m ₀ )=- Kt When m = m ₁ , we get ( m ₁ ~m ₀ )=- Kt t = -1 ~K ( m ₁ ~m ₀ )= 1 ~K ( m ₀ ~m ₁ )