Thread: radioactive/exponential decay

Hi!

I understand the concept of radioactive decay when you have only one element.


But what happens when one element decays into a second element and the second decays into a third. What is the quantity of not decayed material of the second element? And what if you have a longer chain? For example:
Element A has a half-life
Element B has a half-life
Element C is stable.
A decays to B which decays to C.

A(t), B(t), C(t) - is the quantity of A, B, C at time t

B(t)=?
C(t)=?

Hi

Between t and t+dt
A goes from A(t) to A(t+dt) = A(t) - a A(t) dt
B goes from B(t) to B(t+dt) = B(t) - b B(t) dt + a A(t) dt
C goes from C(t) to C(t+dt) = C(t) + b B(t) dt

It is clear that for every t, A(t) + B(t) + C(t) is constant

A(t+dt) = A(t) - a A(t) dt







B(t+dt) = B(t) - b B(t) dt + a A(t) dt





General solution of equation is


Particular solution of is
if a and b are different






To be checked !!
But I think that the general idea is not so far !