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The half life of a radioactive elements is 10 yrs. Calculate the fraction of the sample left after 20 yrs. |
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Answer» Solution :Data supplied, `T_(1//2) = 10 YRS :. t = 20 yrs = 2 xx 10= 2T_(1//2) :. n = (2T_(1//2))/(T_(1//2))= 2` `N = N_0 E^(-lambda t) = N_0 (e^(-lambda T_(1//2)))^(t//T_(1//2)) = N_0.(1/2)^(t//T_(1//2))` Also `N = N_0//2^n` `:. N_0//2^n = N_0 (1/2)^(1//2)` `:. N/(N_0) = 1/(2^n) = 1/4` `:. N = (N_0)/4` i.e., No. of atoms left after 20 yrs = `(N_0)/(4)`, i.e. `1/4 th`of the original no. of atom. |
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