Calculating Atom Density of UO2-ThO2 Fuel

[tony.almeda]

if fuel coposition as follow : 75 wt% Tho2- 25 wt% uo2, were the U enrichment 19.5 w% ... how can i caculate the number density (Atoms/barn-cm) for the comopsition ?

 

[statphys]

If I recall correctly number density of a nuclide is just the number of atoms per unit volume as given by;

N = (Rho * NA) / A

Where; Rho = density (in g/cm^3)
NA = Avagadro number
A = Atomic weight in g

To find the composite for the mixture just weight by the relative proportions of the nuclides in the mixture.

i.e [0.75*N(Thorium)] + [0.25*0.195*N(U-235)] + [0.25*(1-0.195)*N(U-238)]

From your query I wonder if you are really after the macroscopic cross-section which is simply the number density multiplied by the microscopic cross-section (as measured in barns).

 

[raining Pete]

To calculate the number density (atoms/barn-cm) for this fuel composition, you will need to use the following steps:

Step 1: Calculate the molar mass of the fuel composition.

To do this, you will need to know the atomic weight of Th (232.038 g/mol) and U (238.0289 g/mol). You can then use the weight percentages provided to calculate the molar mass of the fuel composition.

Molar mass of ThO2 = (232.038 g/mol + 2 x 15.999 g/mol) = 266.036 g/mol
Molar mass of UO2 = (238.0289 g/mol + 2 x 15.999 g/mol) = 272.0279 g/mol

Molar mass of fuel composition = (0.75 x 266.036 g/mol) + (0.25 x 272.0279 g/mol) = 269.03 g/mol

Step 2: Calculate the number of moles of Th and U in 1 g of the fuel composition.

Number of moles of Th = (0.75 x 1 g) / 266.036 g/mol = 0.002814 mol
Number of moles of U = (0.25 x 1 g) / 272.0279 g/mol = 0.000918 mol

Step 3: Calculate the number density (atoms/barn-cm) using the following formula:

Number density = (Avogadro's number x Number of moles) / (Cross-sectional area in barn-cm)

Avogadro's number = 6.022 x 10^23 atoms/mol
Cross-sectional area of 1 barn-cm = 1 x 10^-24 cm^2

Number density = (6.022 x 10^23 x 0.002814 mol) / (1 x 10^-24 cm^2) = 1.695 x 10^25 atoms/barn-cm (for Th)
Number density = (6.022 x 10^23 x 0.000918 mol) / (1 x 10^-24 cm^2) = 5.530 x 10^24 atoms/barn-cm (for U)

Therefore, the number density for the given fuel composition would be 1.695 x 10^25 atoms/barn-cm for Th