AIPMT 2010 Physics and Chemistry Paper

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=‌

loge2

λ

=‌

loge2

(‌ 1 5 )

=5log02 minutes