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Show that the mass of radium (""_(88)^(226)Ra) with an activity of 1 curie is almost a gram. Given T_(1//2) = 1600 years. |
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Answer» Solution :The activity of the sample at any time t `R = lambda N` Here `lambda = (0.6931)/(T_(1/2))` ` R = 1 Ci = 3.7 xx 10^(10) dis s^(-1)` `T_(1/2) = 1600 year = 1600 xx 3.16 xx 10^(7)` dis `therefore` The amountof RADIUM, `N = (R)/(lambda) = (RT_(1/2))/(0.6931)` ` = (3.7 xx 10^(10) xx 1600 xx 3.16 xx 10^(7))/(0.6931)` ` (18707.2 xx 10^(17))/(0.6931)` `= 26990.62 xx 10^(17)` `N = 2.7 xx 10^(21)` atoms As 226 G of radium CONTAINS `6.023 xx 10^(23)` atoms so the amount of required strength. ` = (226 xx 2.7 xx 10^(21))/(6.023 xx 10^(23))` `= 101.311 xx 10^(-2)` ` = 1.013 g approx 1 g` |
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