# From a radioactive substance 'n' nuclei decay per second at an instant when total number of nuclei are 'N' .Find half life of radioactive substance.

Samyak Jain
333 Points
3 years ago
In radioactive decay, rate of decay (– dN/dt) of nuclei at an instant is proportional to the number of nuclei
present (N) at that instant.
– dN/dt = $\dpi{80} \lambda$.N , $\dpi{80} \lambda$ is constant of proportionality.
Here rate of decay = n  i.e.  – dA/dt = n.
n = $\dpi{80} \lambda$.N  $\dpi{80} \Rightarrow$  $\dpi{80} \lambda$  =  n/N
As we know that half life of radioactive substance is
t1/2 = ln2 / $\dpi{80} \lambda$,  t1/2 = ln2 /(n/N)
t1/2 = N.ln2 / n .