A certain radioactive element has a half-life of 20 years. If we have a block with 10 g of the element in it, after how many years will there be just 2.5 g of the element in the block?

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N = ⇒ e − λ t = ⇒ t = = ​ T 1/2 ​ = 20 years N 0 ​ = 10 g N = 2.5 g N 0 ​ e − λ t λ = T 1/2 ​ 0.693 ​ ln ( N 0 ​ N ​ ) λ 1 ​ ln ( N N 0 ​ ​ ) = 0.693 T 1/2 ​ ​ × ln ( N N 0 ​ ​ ) 0.693 20 ​ × ln ( 2.5 10 ​ ) = 40 years ​

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