There are 10 10 radioactive nuclei in a given radioactive element. Its half-life time is 1 min . How many nuclei will remain after 30 s ? ( 2 = 1 . 414 )

Step-by-step solution

Recall the relationship between the present amount of element and the initial amount of element in terms of the decay constant, N = N 0 e - λ t , now the relation between decay constant and half-life, t 1 2 = 0 . 693 λ , ⇒ N = N 0 e - 0 . 693 t t 1 2 ⇒ N = 10 10 e - 0 . 35 = 7 × 10 9 .