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.

Explanation

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 amount of 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`