Explosive reaction based on reaction rate

### Question



> 
> We have the following chemical reactions:
> 
> 
> $$
> \begin{align}
> \ce{A + B^\* &-> C + D^\*}\tag{1}\\
> \ce{D^\* &-> B^\* + B^\*}\tag{2}\\
> \ce{B^\* &-> B}\tag{3}
> \end{align}
> $$
> 
> 
> If the initial concentrations are $[\ce{A}] = \pu{100e-6 mol cm-3}$ and $[\ce{B}] = \pu{1e-6 mol cm-3}$, is the system explosive? We know that $k\_1 = \pu{1e6 cm3 mol-1 s-1},$ $k\_2 = \pu{50 s-1}$ and $k\_3 = \pu{25 s-1}.$
> 
> 
> 


### My solution


So I found the rate expressions for $\ce{A}$ and $\ce{B},$ by applying steady-state approximation (SSA) on $[\ce{D^\*}].$ I get the following expressions:


$$
\begin{align}
\frac{\mathrm d[\ce{A}]}{\mathrm dt} &= -k\_1 \cdot [\ce{A}] \cdot [\ce{B^\*}]\\
\frac{\mathrm d[\ce{B}]}{\mathrm dt} &= (k\_1 \cdot [\ce{A}] - k\_3) \cdot [\ce{B^\*}]
\end{align}
$$


Upon entering the numbers into the above expressions, I get the following numbers:


$$
\begin{align}
\frac{\mathrm d[\ce{A}]}{\mathrm dt} &= \pu{-\frac{1}{10000} mol cm-3 s-1}\\
\frac{\mathrm d[\ce{B}]}{\mathrm dt} &= \pu{\frac{3}{40000} mol cm-3 s-1}
\end{align}
$$


My conclusion was that the system is not explosive since the rate of formation of $\ce{B}$ is quite low. Since if the rate is too low, then the reaction can not be considered explosive.


But the problem with my explanation is that I would like to have a reference number. Is there a reference such as f.e. rate higher than $10$ is considered explosive, etc? I have tried looking everywhere but could not find any 'value.' Could anyone provide some insight into this:


* Are my explanation and conclusion correct?
* Is there a reference value for explosive reactions?


I have an additional question. What is the connection between an explosive system and the steady-state approximation? If the system is explosive, can I still use SSA or does it become invalid?


