According to activity law R=R0e−λt...(i) where, R0= initial activity at t=0 R= activity at time t λ= decay constant According to given problem, R0=N0 counts per minute R=N0/e counts per minute t=5 minutes Substituting these values in equation (i), we get
N0
e
=N0e−5λ e−1=e−5λ 5λ=1 or λ=
1
5
per minute At t=T1∕2, the activity R reduces to
R0
2
. where T1/2= half life of a radioactive sample From equation (i), we get
R0
2
=R0e−λT1/2 eλT1/2=2 Taking natural logarithms of both sides of above equation, we get λT1,2=log62 or T1/2=