VITEEE 2014 Paper

After n half-lives

N

N0

= (

1

2

)n = (

1

2

)t∕7
N = N+

0

e

=

cN0

cN0

= (

1

2

)5∕7
⇒

1

e

= (

1

2

)5∕7
Taking log on both sides, we get
log 1 - log e =

5

7

log

1

2

- 1 =

5

7

(- log 2)
T = 5loge2
Now, let t’ be the time after which activity reduces to half
(

1

2

) = (

1

2

)1′∕5loge2
t' = 5 loge 2