Class 12 NEET Physics Atoms and Nuclei Questions Part 2

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 couts 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=T

1

2

the activity R reduces to

R0

2

where T

1

2

= half life of a radioactive sample
From equation (i), we get

R0

2

=R0e−λT

1

2

eλT

1

2

=2
Taking natural logarithms on both sides of above equation,we get
λT

1

2

=loge2
or T

1

2

=

loge2

λ

=

loge2

( 1 5 )

=5loge2 minute