Relationship between the number of fuel elements and criticality

[Januar]

I usually do not ask for this kind of stuff, but this time I really have no way to verify if this is correct(and it has to be). So here it goes: On a subcritical nuclear reactor with 100 fuel elements we read the signal of 10e-9 A. When we add 10 more fuel elements, signal jumps to 10e-8 A. How many rods do we have to add, to make the reactor critical? So, I know the relationships between reactivity/neutron flux/criticality/signal, but I have no idea how are they dependend on the number of fuel elements?

Usually, I would have to solve the diffusion equation, but this exercise gives no data about reactor geometry, so.. do you guys have any idea what this could be about?

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Could the admin move this to Homework section please? I have not seen it before..

 

[Vanadium 50]

Moved .

Now, how far have you got?

 

[Vanadium 50]

Moved .

Now, how far have you got?

 

[Januar]

Moved .

Now, how far have you got?

Well I know that $I \propto \frac{1}{1-k}$, where I is the signal on the detector. But I can only guess how I is dependent on the number of fuel elements(increases by an order of magnitude for each 10 rods?) .