Calculate the time interval between 33 % decay and 67 % decay if half-life of a substance is 20 min .

Step-by-step solution

N 1 = N 0 e - λ t 1 N 1   N 0 = e - λ t 1 0 . 67 = e - λ t 1 ln 0 . 67 = - λ t 1   N 2 = N 0 e - λ t 2 N 2   N 0 = e - λ t 2 0 . 33 = e - λ t 2 ln 0 . 33 = - λ t 2 ln 0 . 67 - ln 0 . 33 = λ t 1 - λ t 2 λ t 1 - t 2 = ln 0 . 67 0 . 33 λ t 1 - t 2 ≅ ln 2 t 1 - t 2 ≃ ln 2 λ = t 1 / 2 Half life = t 1 / 2 = 20 minutes.