A `""^118Cd` radio nuclide goes through the transformation chain. `""^118Cd underset(30min) rarr^(118)In underset(45min)rarr^(118)Sn ("stable")` The half-lives are written below the respective arrows. At time `t=0` only Cd was present. Find the fraction of nuclei transformed into stable over `60` minutes.

A `""^118Cd` radio nuclide goes through the transformation chain. `""^

1.	A `""^118Cd` radio nuclide goes through the transformation chain. `""^118Cd underset(30min) rarr^(118)In underset(45min)rarr^(118)Sn ("stable")` The half-lives are written below the respective arrows. At time `t=0` only Cd was present. Find the fraction of nuclei transformed into stable over `60` minutes.
Answer» Correct Answer - A::C At time `t=t`, `N_1=N_0e^(-lambda_1t)` and `N_2=(N_0lambda_1)/(lambda_2-lambda_1)(e^(-lambda_1t)-e^(-lambda_2t))` `:.` `N_3=N_0-N_1-N_2` `=N_0[1-e^(-lambda_1t)-(lambda_1)/(lambda_2-lambda_1)(e^(-lambda_1t)-e^(-lambda_2t))]` `:.` `N_3/N_0=1-e^(-lambda_1t)-(lambda_1)/(lambda_2-lambda_1)(e^(-lambda_1t)-e^(-lambda_2t))` `lambda_1=0.693/30=0.0231 mi n^(-1)` `lambda_2=0.693/45=0.0154mi n^-1` and `t=60min` `:.` `N_3/N_0=1-e^(-0.0231xx60)-(0.0231)/(0.0154-0.0231)(e^(-0.0231xx60)-e^(-0.0154xx60))` `=1-0.25+3(0.25-0.4)` `=0.31`

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