IIT JEE Advanced 2010 Paper 2

We have the radioactive decay
N = N0e−λt
Therefore,
ln(

dN

dt

) = ln(N0λ)−λt
The slop of the curve gives the value of λ:
λ =

1

2

per year
Therefore, the number of radioactive nuclei in given time t = 4.16 years is given by
N (4.16) = N0e−(

1

2

)×4.16 = 0.124 N0
Hence, p =

N0

N(4.16)

=

1

0.124

= 8