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A .^118Cd radio nuclide goes through the...

A `.^118Cd` radio nuclide goes through the transformation chain.
`.^118Cdunderset(30min)rarr^(118)1n underset(45min)rarr^(118)Sn (stabl e)`
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.

Text Solution

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`N_(1)=N_(0)e^(-lamda_(1)t)and N_(2)=(N_(0)lamda_1)/(lamda_(2)-lamda_1)(e^(-lamda_(1)t)-e^(-lamda_(2)))`
`:.N_(3)=N_(0)-N_(1)-N_2`
`N_(0)[1-e^(-lamda_(1)t)-lamda_(1)/(lamda_(2)-lamda_1)(e^(-lamda_(1)t)-e^(-lamda_(2)t))]`
`:.N_3/N_0=1-e^(lamda_(1)^(t))-lamda_1/(lamda_(2)-lamda_(1))(e^(-lamda_(1)t)-e^(-lamda_(2)t))`
`lamda=(0.693)/30=0.0231"min"^(-1)`
`lamda_(2)=(0.693)/45 = 0.0154 "min"^(-1) and t = 60` minutes .
On substituting the given values `N_3/N_0 =0.31 `.
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