- Radioactivity is a nuclear phenomenon
- When a nucleus disintegrates by emitting a particle ( α and β) or by capturing an electron from the atomic shell( K-shell) ,the process is called radioactive decay. This decay process is spontaneous.
- Let us take a radioactive sample containing N
_{0}at time t=0 i.e, at the beginning. We wish to calculate the number N of these nuclei left after time t. - The number of nuclei of a given radioactive sample disintegrating per sec is called the activity of that sample is

dN/dt=rate of decrease of nuclei with time=Activity of sample at time t --(1) - Experimentally it is found that the activity at any instant of time t is directly proportional to the number N of parent type nuclei present at that time

Where λ > 0 is proportionality constant and negative sign indicates that N decreases as t increases - From equation (2) we get

i.e. ,λ is fractional change in N per sec

=> λ is not merely a proportionality constant ,but it gives us the probability of decay per unit interval of time - Hence λ is called the probability constant or decay constant or disintegration constant
- dN is the no of parent nuclei that decay between t and t+dt and we have taken N as continuous variable
- From (2)

N_{0}=No of radioactive nuclei at t=0 - From (4) we see that law of radioactive decay is exponential in character
- From figure it can be noted that only half the amount of radon present initially after 3.83 days and 1/4 after 7.66 days and so on
- Plot shows that in a fixed time interval a fixed fraction of the amount of radioactive substance at the beginning of interval decays
- This faction is independent of the amount of radioactive substance and depends only on the interval of the time
- The decay constant λ is a characteristics of radioactive substance and it depends in no way on the amount of the substance present

## 0 Comments