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The half-life of ""_(92)^(238)U undergoing alpha-decay is 4.5 xx 10^9 years. What is the activity of 1g sample of ""_(92)^(238)U ? |
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Answer» Solution :`T_(1//2) = 4.5 xx 10^9 y = 4.5 xx 3.16 xx 10^7 s//y` `= 1.42 xx 10^(17) s` One k mol of any isotope CONTAINS Avogadro.s number of atoms, and so 1g of `""_(92)^(238)U` contains `1/(238 xx 10^(-3)) kmol xx 6.025 xx 10^(26) "atom"//kmol = 25.3 xx 10^(20) "atoms"` The decay rate R is `R = lambda N = (0.693)/(T_(1//2)) N` `= (0.693 xx 25.3 xx 10^(20))/(1.42 xx 10^(17)) s^(-1) = 1.23 xx 10^4 s^(-1) = 1.23 xx 10^4 BQ`. |
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