Question

The element K decays into Ar and Ca (via beta plus/minus decay). At t=0 you got from element K N times and zero from Ar and Ca. Ar and Ca have different decay constants.
Find N_Ar(t) and N_Ca(t).

I can't find anything because terms always seem to cancel. Can anybody help?
As far as I know the decay constant of K is the sum of the decay constant of Ar and Ca but I couldn't use that to my advantage. :(

Answer 1

I meant N_K(t=0)=N

I can't even find a useful differential euqation because the terms cancel but I found out that (not to my surprise) N_K(t)=N*e^(-Lamba_K*t) ...

Answer 2

Here is what I got so far

Answer 3

*

Answer 4

?