Half Life (t1/2)= 40 days
Now,
Decay Constant =$\lambda = \frac{{0.693}}{{{t_{\frac{1}{2}}}}}$
$ = \frac{{0.693}}{{40{\rm{ }}days}}$
$\begin{array}{l} = \frac{{0.693}}{{40 \times 24 \times 60 \times 60}}\\ = 2.005 \times {10^{ - 7}}\end{array}$
N0 = 1012 atoms
And,
The Disintegration rate in 1 second
= Rate of Disintegration
=$\frac{{ - dN}}{{dt}} = \lambda {N_0}$
$\begin{array}{l} = 2.005 \times {10^{ - 7}} \times {10^{ - 7}}\\ = 2.005 \times {10^5}\end{array}$
The number of disintegrations in one second is $2.005 \times {10^{ - 5}}$