# Inventory of Cs-137

Problem:
Reactor operating at 2300 MW with specific power of 24.42 MW/MT, was shutdown on 1 January 2009. The reactor was fueled with 93.3 MT of uranium with initial enrichment of 3.8% U-235. At shutdown, core burnup 23.3 GW-day/MT.
Question:
1.What was inventory of Cs-137 when the reactor was shutdown?
2.How much Cs-137 will be left on 4 March 2009?

Actions:
Honestly, i have hard time understanding what is going here.
1.I thought that this is how many moles of the fission product Cs-137 does this reactor produce per day?
2.How much left is N(t)=N0*(0.5)t/t0.5? I need to plug in t here 4 March 2009 - 1 January 2009. Right?
Steps:
1. 1 mole fissioned =223 MWD
2300/223= 10.31 moles of fissioned per day
6.19 atoms of Cs-137 per 100 fissions.
10.31*0.00619=.6384304 moles of Cs-137 produced per day.
A=λN=(ln2)(.60222*1024)*(1/(365*24*3600*30.07))
Am i on the right track?

## Answers and Replies

anorlunda
Staff Emeritus
Are there any other fission products that might decay into CS137?

DEvens
You are on the right path. However, I don't know what the application is so I can't tell you if your assumptions are correct (is this a HW problem, or a real application?). Some things to think about

1. You are assuming a constant fission yield of Cs-137. This may be appropriate, but a specific fuel enrichment was given. To calculate a better fission yield, you would need to know what isotopes were in the core (U-235, U-238, Pu-239, etc.) This would require a detailed burnup calculation.

2. You are assuming the Cs-137 was not decaying as it was built up. This may be appropriate with the longer half-life, but there is also a fairly simple equation to calculate the build-up of a radioactive nuclide from a constant source (which I'm not giving here)

3. I'm not sure where the "1 mole=223 MWD" is coming from. It may be an appropriate rule of thumb, but there are more detailed ways to calculate this. As with the first point, you may need a detailed burnup calculation to know the specific isotopes in the core.

4. Either your Cs-137 yield is off by a factor of 10, or you are missing a factor of 10 when converting to percentage.

5. Finally, your activity equation is not quite correct. You are missing a term, and I highly recommend including units.

I just noticed that the original post was from 2011. I assume he eventually figured it out :)