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Counting rate from a radioactive source is 8000 cts per sec. at time t = 0 and after 10 minutes decay is 1000 cts/sce. Calculate (i) half life period, (ii) decay constant and (iii) counting rate after 20 minutes. |
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Answer» Solution :Data supplied, i `N_0 = 8000 cts//"sec", "" t_1 = 10 "minutes", "" N = 1000 cts//"sec"` `N/(N_0) = 1/(2^n)` `:. 1/(2^n) = 1000/8000 = 1/8 = 1/(2^3)` `:. 2^n = 2^3 , "" n = 3` `t_1 = nT_(1//2) "" :. "" T_(1//2) = (t_1)/n= 10/3 "minutes" = 200 "sec"` i.e. Half LIFE period = `10/3` minutes = 200 sec ii. Decay constant `lambda = (0.6931)/((10//3)) = 0.2079` per minute iii. `t_2 = 20 "min" :. t_2 = NT, "" n = (t_2)/(T_(1//2)) = 20/((10//3)) = 6` `:. N/(N_0) = 1/(2^n) = 1/(2^6) = 1/64` `N = (N_0)/64 = 8000/64= 125 cts//"sec"` . |
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