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Obtain the expression for the half-life of a radioactive element. |
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Answer» SOLUTION :It is defined as the time period during which half of the original atoms of the radiactive elementdisintegrate. LET `N_0` be the initial number of atoms of a radioactive sample. After a time INTERVAL EQUAL to the half life T , the number of atoms of the radioactive sample remaining will be `N_0/2`. Then `N=N_0/2` at `t=T_1//2` (A LUTTE bigger if possible not early visible ) w.k.t `N=N_0e^(-lambdat)` `cancelN_0/2=cancelN_0e^(-lambdaT_1//2) rArr 1//2=e^(-lambdaT_1//2) rArr 1/2=1/(e^(lambda)T_1//2) rArr 2=e^(lambda)T_1//2` `lambdaT_1//2=log_e^2 rArr T_1//2=2.303log_10^2=2.303xx0.3010`=0.693 `T_(1//2)=0.693/lambda` |
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