What is the half-life period of a radioactive material if its activity drops to 1 16 th of its initial value of 30 years ?

Step-by-step solution

Activity of a radioactive material is given by A = A 0 e - λ t , here, λ - is decay constant. Taking logarithmic function both sides, ⇒ - λ t = ln A A 0 Using relation between half life and decay constant, ⇒ - ln 2 t 1 2 × 30 = ln 1 16 ⇒ - ln 2 t 1 2 × 30 = - 4 ln 2 ⇒ t 1 2 = 30 4 = 7 . 5   yrs