Modern Physics 3 Question 38
37. A radioactive nucleus decays to a nucleus with a decay constant further decays to a stable nucleus with a decay constant . Initially, there are only nuclei and their number is . Set-up the rate equations for the populations of and . The population of nucleus as a function of time is given by . Find the time at which is maximum and determine the populations and at that instant.
(2001, 5M)
Show Answer
Solution:
- (a) Let at time
, number of nuclei of and are and . Then,
Rate equations of the populations of
(b) Given
For
Substituting the values of
(c) The population of