Define the term ‘decay constant’ of a radioactive sample. The rate of disintegration of a given radioactive nucleus is 10000 disintegrations/s and 5,000 disintegrations/s after 20 hr. and 30 hr. respectively from start. Calculate the half-life and initial number of
nuclei at t = 0.
Decay constant of a radioactive substance is the ratio of the rate of change of the number nuclei at any given time in the sample to the number of nuclei in the sample at that time :
Let the number of nuclei be N. and be the decay constant.
We know that,
On equating the given values, we get
On dividing both the equations (a) and (b) we have
On taking in both sides, we have
The half-life is -
Now, let's find
Now,