Macroscopic Absorption Cross-Section

[Naimbora]

The compositions of nuclear reactors are often stated in volume fractions. i.e the fractions of the volume of some region that are composed of particular materials. Show that the macroscopic cross section for the equivalent homogeneous mixture of materials is given by

∑a = f1 ∑a1 + f2∑a2 + …..

where fi and ∑ai are respectively the volume fraction and macroscopic absorption cross section of the ith constituent at its normal density.

 

[Naimbora]

I took a look at John Lamarsh's book; Int. to Nuclear Engineering but there is not a exact clue to solve tihs problem.. Also i could got nothing on the net. Its very simple to make a prediction about this but what is the exact proof behind this situation..