A block having 12 g of a radioactive element is placed in a room. This half-life of the radioactive element is 15 years. After how many years there will 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 ln ( 8 ) = 15 0.693 × 3 × ln 2 = 15 × 3 = 45   y e a r