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State the law of radioactive decay. 3/4t...

State the law of radioactive decay. 3/4th of a radioactive sample decays in 3/4 s. What is the half-life of the sample?

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The rate of decay of a radioactive sample with respect to time is proportional to the number of radioactive atoms present in the sample at that instant . This is the law of radioactive decay. As per this law, if `N_0` be the number of atoms of a certain radioactive element initially, and N be its number after a time t, then
`N=N_0 e^(-lambdat)` ( where `lambda`=radioactive decay constant )

Given `3/4`th of the sample decays in `3/4`s.
So, `2T=3/4` s or , T=`3/8`s
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The initial number of radioactive atoms in a radioactive sample is N_0 . If after time t the number of becomes N, then N=N_0e^(-lambdat) , where lambda is known as the decay constant of the element. The time in which the number of radioactive atoms becomes half of its initial number is called the half-life (T) of the element. The time in which the number of atoms falls to 1/e times of its initial number is the mean life (tau) of the element. The product lambdaN is the activity (A) of the radioactive sample when the number of atoms is N. The SI unit of activity is bequerel (Bq)' where 1 Bq = 1 decay. s^(-1) . The half-life of Iodine-131 is 8 d. Its mean life (in SI) is - (A) 4.79xx10^5 s. (B) 6.912xx10^5 s. (C) 9.974 xx 10^5 s. (D) 22.96xx10^5 s.