A nucleus has a half-life of 30 minutes. At 3 PM its decay rate was measured as 120,000 counts/sec. What will be the decay rate at 5 PM ?

Step-by-step solution

Given T =30 minutes. d N dt =120 ~K counts sec After each half life, activity is reduced to half therefore after n half lives activity reduces to ( 1 2 )^ n . Also dN dt N dN dt at 5 P . M . will be equal to activity remaining after four half lives. i.e. ( 1 2 )⁴= ( 1 16 th ) of the initial activity ( dN dt )_ at 5 PM = ( 1 16 . th ) of the initial activity array l ( dN dt )_ 5 P _ . M = ( 1 16 ) ( d N dt )_ 3 PM array