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) Two radioactive nuclei having half life periods 20 years and 15 years respectively have initialactivities in the ratio 1 : 2. After how many years,both posses equal activity? |
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Answer» ber of years after which the 2 nuclei will have the same activity is 60Number of Nuclei at a time is given by N =N0. at t = T, half life period, N = N0/2 N/N0 = = 1/2natural LOG, LN(1/2) = -LTln 2 = LT ==> L = 0.693/TLet L be the DECAY constant and T be the half lifeIf a and b are the 2 nuclei,La = 0.693/Ta and Lb = 0.693/TbLa = 0.03465 , Lb = 0.0462Activity of the nuclei is given by R = = -LN0 = -LN.Therefore given ratio of initial activities: = To find the time when both have equal activity,Ra = Rb -LaNa(0) = -LbNb(0)rearranging ==> ln 2 = (Lb - La)t==>t = ln 2/ (Lb - La) = ln 2/(0.0462 - 0.03465) = 60 years |
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