# Equation of radionuclide production

The equation of radionuclide production is as follow
dN/dt = k - λN

All my textbook assumes that k is a constant vale.
http://jol.liljenzin.se/KAPITEL/CH15NY3.PDF

for the equation to be valid,
(iii) the flux is not decreased ... . ..
Corrections must then be introduced.

Please advise me that is there any reference that doing this correction.
What form of the equation will be, is there analytic solution ?

## Answers and Replies

mfb
Mentor
Well, your k will become a k(t) where the details depend on the production process. If the production process is the decay of another nuclide, your k(t) follows the exponential decay of this, for example.

k usually represents a source of isotopes from nuclear fission in a reactor.
In this case, k equals the fission yield of the isotope times the total fission source.
The fission source is relatively constant, so k is relatively constant for a given isotope.

I am assuming that you are learning about radioactive decay. In later courses, you will learn
about general depletion and k will be defined explicitly.