Question

$1$ milligram radium has $2.68\times {10}^{18}$ atoms. Its half life period is $1620$ years. How many radium atoms will disintegrate from $1$ milligram of pure radium in $3240$ years?

Answer 1

Number of half lives in $3240$ years $=\frac{3240}{1620}=2$
Amount of radium left after two half lives $=1\times {\left(\frac{1}{2}\right)}^2$$=0.25mg$
Amount of radium disintegrated $=(1-0.25)=0.75mg$
Number of atoms which have disintegrated $=0.75\times 2.68\times {10}^{18}$$=2.01\times {10}^{18}$