From equation of radioactivity we know At=A0e−λt Where At= Amount of material at time 't' A0= Amount of substance at t=0 λ= decay constant t= time. Taking log we have ln[‌
A0
At
]=λt For half life At=‌
A0
2
. ⇒ln‌2=λt1∕2‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(A) t1∕2= half life From given condition. ln[‌