"Magic Merv" and Criticality

[richphys]

Homework Statement

In terms of criticality "magic merv" stands for the nine parameters which determine the level of criticality in a system: mass, absorption, geometry, interaction, concentration, moderation, enrichment, reflection and volume.

The topic is decomissioning plutonium nitrate waste from a dissolver.

I am stuck on the "mass" part when applying "magic merv". I think I cannot work out critical mass with the data I have (below). Is there anything I can calculate? Any graphs regarding plutonium nitrate and critical mass in cylinders would be helpful.

Homework Equations

Plutonium nitrate exists in concentrations < 1 Kg/L
The total mass of plutonium nitrate is unknown.
There will be 36.5 gallons of plutonium nitrate waste from the dissolver.
The plutonium nitrate waste will be moved from the dissolver to 30 gallon drums measuring 39.25 inches in height by 27 inches in diameter.
Raschig rings will be added in concentrations from 4-85 g/L

The Attempt at a Solution

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[NateD]

I am not sure what to do at this point. Any advice would be appreciated. The mass of plutonium nitrate is the first factor in "magic merv", so you need to calculate the total mass of plutonium nitrate in the waste before you can proceed. You can calculate this by multiplying the concentration of plutonium nitrate (kg/L) by the volume of waste (L). You can also calculate the mass of plutonium nitrate in each drum by multiplying the concentration of plutonium nitrate (kg/L) by the volume of each drum (L). Once you have calculated the mass of plutonium nitrate in each drum, you can then determine the critical mass of plutonium nitrate in each drum. This is done by calculating the criticality index, which is a measure of the criticality of a material. The criticality index is calculated by dividing the mass of plutonium nitrate in the drum by the sum of the volumes of the Raschig rings and the drum. For example, if the mass of plutonium nitrate in a drum is 1 kg and the total volume of the Raschig rings and the drum is 100 L, then the criticality index is 0.01. This indicates that the critical mass of plutonium nitrate in the drum is 1 kg. Once you have calculated the critical mass of plutonium nitrate in each drum, you can then use this information to create graphs or diagrams that show the critical mass of plutonium nitrate in each drum. This will help you understand the potential risk of the waste and decide how to safely decommission it.