Problem Borated stainless steel has the density of 7.74 g/cm3. This alloy is wid

ID: 3281508 • Letter: P

Question

Problem Borated stainless steel has the density of 7.74 g/cm3. This alloy is widely used for applications where neutron absorption is needed. Typical applications include racks for wet storage of used nuclear fuel, baskets for casks used for dry storage of used nuclear fuel, glove box components, and a general reactor shields. manganese 2%, chromium 20%, nickel 12%, and the remainder is iron. incident on a 2.5 cm2 target made of the borated stainless steel. The weight percent composition of this steel: natural-abundance boron 2% A beam of 0.0253-eV neutrons with the intensity of 2.4x10' neutrons/(cm2-s) is a) Calculate the atomic densities of boron-10 and boron-11, manganese, b) Calculate the macro pic cross-sections: absorption (L), scattering (L), and c) How thick must the target be to reduce the intensity of the uncollided 0.0253-ev d) How many neutron interactions per second happen in the target of the thickness chromium, nickel, and iron in the target material total () for the target material at the neutron energy 0.0253 eV neutron beam by a factor of 4? determined in (c)?

Explanation / Answer

So,

Density of 10_B = 4.3191*10^21 atoms/cm3

Density of 11_B = 4.5046*10^21 atoms/cm3

Density of Mn = 1.6968*10^21 atoms/cm3

Density of Cr = 17.92*10^21 atoms/cm3

Density of Ni = 9.53*10^21 atoms/cm3

Density of Fe = 53.41*10^21 atoms/cm3

Here @ is Coefficient and N is element density

For finding @ = (Mu)(atomic mass of element)/(mass Density)(NA)

Now Mu = 1/wavelength

Wavelength = (plank constant)(Speed of light)/Energy

SO mass density of elements

Let target be 1000 g,

Volume = 1000/7.74 = 129.2 cm3

So as per percentage Fe = 640 g, Cr = 200g, Mn = 20 g, B = 20 g ( 10_B = 4 g & 11_B = 16 g ),

Ni = 120 g

Density of 10_B = 4/129.2 = 0.031 g/cm3

Density of 11_B = 16/129.2 = 0.1238 g/cm3

Density of Mn = 20/129.2 = 0.1547 g/cm3

Density of Cr = 200/129.2 = 1.5479 g/cm3

Density of Ni = 120/129.2 = 0.9287 g/cm3

Density of Fe = 600/129.2 = 4.6439 g/cm3

So,