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

Step-by-step solution

aligned & Given, T_ 1 / 2 =15 yr & N₀=12 ~g & N=1.5 ~g & N=N₀ e ^ - t & aligned array rlrl & & e^ - t & = N N₀ & - t & = ( N N₀ ) & & t & = 1 ( N₀ N )= T_ 1 / 2 0.693 ( N₀ N ) array [ = 0.693 T_ 1 / 2 ] aligned & = 15 0.693 ( 12 1.5 ) & =45 yr aligned