A block having 12 g of an element is placed in a room. This element is a radioactive element with a half-life of 15 years. After how many years will there be just 1.5 g of the element in the box?

Step-by-step solution

Given, T 1 2 = 15 y e a r N 0 = 12 g N = 1.5 g ∴ N = N 0 e - λ t ⇒ e - λ t = N N 0 ⇒ - λ t = ln ⁡ N N 0 ⇒ t = 1 λ ln ⁡ N 0 N = T 1 2 0.693 ln ⁡ N 0 N ∵ λ = 0.693 T 1 2 = 15 0.693 × ln ⁡ 12 1.5 = 15 0.693 ℓ n ( 8 ) = 15 0.693 × 3 × ℓ n 2 = 15 × 3 = 45 y e a r