Relation of atomic and mass enrichment?

[OneMoreName]

Hi all,

I am preparing for a job interview in some nuclear facility and have to refresh my knowledge about nuclear stuff. So I started reading the book of Lewis "Fundamentals of reactor physics". I got stuck at page 35, formula (2.24). Does anyone have a clue how to arrive at this equation? Where does this factor 0.0128 come from? I played with the formulas a lot but never arrive at this equation. Help would be really appreciated guys. Since I am not allowed to put a link, please put a http: inside the following and you will see the page.

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[Bill_K]

Replace the N's in favor of the M's. Up to a constant factor, N ~ M/A, so Eq 2.20 is

e_a = (M²⁵/235)/((M²⁵/235) + (M²⁸/238))

Then get rid of the M's in favor of e_w:

M²⁵ = e_w(M²⁵ + M²⁸)
M²⁸ = (1 - e_w)(M²⁵ + (M²⁸)

This gives you

e_a = (e_w/235)/((e_w/235) + ((1 - e_w)/238)))

so now just multiply out.

 

[Astronuc]

The calculation of macroscopic cross-section requires atomic density, and enrichment on an atomic basis would be necessary. For manufacturing and accountability, the mass-based enrichment is required, since it is much easier to measure mass, and accountability records are provided in terms of mass.

Bill K provided the method to compare mass fraction with atomic fraction.

Remember that for an element or isotope, N = ρA/M, where ρ = density, A = Avogadro's Number, and M = atomic mass (of the element, which is weight by isotopic fractions, or by isotopic mass, if ρ is the isotpic mass density).

Try 238/235.

 

[OneMoreName]

Oh yes, thanks! I was fooling around with the densities because it is mentioned in the text but this leads to nowhere.

 

[alphy]

Hello,

The equation you are referring to is most likely the relation between atomic and mass enrichment in uranium isotopes. This is an important concept in nuclear science, particularly in the process of enriching uranium for use in nuclear reactors.

The factor of 0.0128 comes from the relative atomic mass of uranium-235 (235.0439) and uranium-238 (238.0508). This factor is used to calculate the atomic enrichment level, which is the ratio of the number of uranium-235 atoms to the total number of uranium atoms in a sample.

The equation is derived from the principles of isotopic abundance and atomic weight. Without going into too much detail, the relative abundance of isotopes in a sample can be determined using mass spectrometry, and this information is then used to calculate the atomic weight of the sample.

I hope this helps in your preparation for your job interview. Good luck!