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

Activity = `(dN)/(dt)` 1 curie = `3.7xx10^(10)` disinetegration per second , Half life of Radium = 1600 years
`lamda=(0.6391)/(T_(1//2)),lamda=0.6931/1600` per year
`=0.6931/(1600xx365xx24xx60xx60)` per second
From law of disintegration
`(dN)/(dt)=lamdaN,N=(dN)/(dt)xx1/lamda`
`(dN)/(dt)=3.7xx10^(10)` disintegrations/second
`thereforeN=3.7xx10^(10)xx1600/0.6931xx365xx24xx60xx60`
= `3.7xx10^(10)xx1.443xx1600xx365xx24xx60xx60`
`N=2.694xx10^(21)` atoms
According to Avogadro.s principle
Mass of `6.023xx10^(23)` atoms give : 226 gm of radium
`therefore` Mass of `2.694xx1021` atoms will give
`=(226)/(6.023xx10^(23))xx2.694xx10^(21)=1.011` gm.
`therefore` The mass of radium with an activity of 1 cuire is almost 1 gram.