Radium `226` is found to have a decay constant of `1.36 xx10^(-11)` Bq.
Determine its half-life in years. If a `200 g` sample of radium was taken in `1902`, how much of it will remain a hundered years later?

Explanation

Given: `lambda=1.36 xx10^(-11) decays s^(-1)` The half-life is
`T_(1//2) =0.(693)/(lambda) =(0.693)/(1.36 xx10^(-11)) =5.096 xx 10^(10)s`
`=1.62 xx10^(3) years`
As initial mass `m_(0)=200g`,
The mass at time `t(=100 years =3.15 xx10^(9) s)` is
`m=m_(0) e^(- lambda t)=(200)e^(-1.36 xx 10^(-11) xx 3.15 xx10^(9))`
`=(200)(0.958)=192 g`