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?) .

 

[rezeew]

I cannot verify the accuracy of this information without more specific data about the reactor and its geometry. However, in general, the number of fuel elements in a nuclear reactor can affect its criticality. Adding more fuel elements increases the number of neutron interactions, which can lead to a higher neutron flux and potentially increase the reactivity of the reactor. This can result in a higher signal being detected, as seen in the given scenario.

In order to determine how many fuel elements would need to be added to make the reactor critical, we would need to know the specific characteristics of the reactor, such as its geometry and fuel type. This information would be necessary to perform calculations and solve the diffusion equation, as mentioned in the provided content.

Without this additional information, it is difficult to accurately determine the relationship between the number of fuel elements and criticality in this scenario. It is important to have all relevant data and to perform calculations carefully in order to ensure the safe and efficient operation of a nuclear reactor.