Calculate the half life and mean life of Radium -226 of activity 1Ci, Given the mass of Radium - 226 is 1 gram and 226 gram of radium consists of `6.023xx10^23` atoms.

Explanation

Activity of 1 gram of radium is `A=3.7xx10^10` distingration per second [i.e., `1Ci=3.7xx10^10` disintegration per second]
No. of atoms in 1 gram of radium is
`N=(6.023xx10^23)/226=2.665xx10^21`
Using `A=lambdaN`
`lambda=A/N=(3.7xx10^10)/(2.665xx10^21)=1.388xx10^(-11)` per second
Half - life of radium is
`T=0.693/lambda=0.693/(1.388xx10^(-11))`
`T=0.499xx10^11` second
`=4.99xx10^10` second
Mean - Life , `tau=1/lambda=1/(1.388xx10^(-11))`
`=0.720xx10^11` second
`tau=7.20xx10^10` second.