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A radioactive isotope X has a half life ...

A radioactive isotope X has a half life of 3 seconds. At t=0, a given sample of this isotope contains 8000 atom. Calculate (i) its decay constant (ii) average life (iii) the time `t_1`, when 1000 atoms of the isotope X remain in the sample (iv) number of decay/sec in the sample at `t=t_1sec.`

Text Solution

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Here, `T=3s, N_0=8000`
(a) `lambda=0.6931/T=0.6931/3sec^-1=0.231s^-1`
(b) form `N/(N_0)=(1/2)^(t_1//T)=1000/8000=1/8=(1/2)^3`
`(t_1)/T=3, t_1=3T=3xx3s=9s`
(c) `-(dN)/(dt)=lambdaN=0.231xx1000=231decay//sec`
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