What is the difference between radioactive equilibrium and transient equilibrium?

Question

Consider the following radioactive decay:

$\ce{A\rightarrow B\rightarrow C}$

In my textbook, it is written that radioactive equilibrium is when rate of formation of $\ce{B}$ is equal to rate of disappearence of $\ce{B}$. In my textbook, it is also written that when the net formation of $\ce{B}$ is zero, we say that the system is in transient equilibrium i.e. $\frac{dB_{N}}{dt}=0$ where $B_{N}$ is the number of atoms of $\ce{B}$ at time $t$. Now, $\frac{dB_{N}}{dt}=0$ means that the rate of formation of $\ce{B}$ is equal to the rate of disappearance of $\ce{B}$ which is exactly what radioactive equilibrium is. Then, what is the difference between radioactive equilibrium and transient equilibrium? Is there even any difference between them? Pleas explain. I am confused.

Answer 1

I guess you have been caught in a semantic trap. Adjectives radioactive and transient describe two different aspects of the same thing.

It could be as well written as "radioactive transient equilibrium". Or, even better as "radioactive steady state", as it is not true equilibrium.

Radioactive describes its nature . It may not be radioactive,by can be thermal, chemical, radiative, mechanical etc .

Transient describes its dynamics. It need not to be transient ( temporary, also called a steady state ), but it can be a permanent, timeless, true equilibrium.