# Equation of radionuclide production

1. Jul 11, 2014

### flied

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 ?

2. Jul 13, 2014

### Staff: 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.

3. Oct 19, 2014

### rpp

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.