The half life of radium is 1500 years. After how many years will one gram of pure radium (i) reduce to 1 centigram? (ii) lose one milligram?
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Here, T=1500yrs, t=? `N/(N_0)=(10^-2g)/(1g)=10^-2=(1/2)^n=1/100` `:. n=(log1-log2)=log1-log100` `n(0-0.3010)=0-2, n=2/0.3010=6.6445` As `n=t/T` `:. t=nT=6.6445xx1500=9967years.` (ii) `N/(N_0)=(1-10^(-3))/1=0.999=(1/2)^n` `:. n(log_e1-log_e2)=log_e0.999` or `n(0-0.6931)=-1.0005`, `n=1.0005/0.6931=1.4435` As `n=t/T :. t=nT=1.4435xx1500yrs` `=2165.2 years`
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