(Solved): Calculate the macroscopic cross-section for scattering of 0.0253eV neutrons i ...

Expert Answer

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This question is related to the behavior of neutrons in water, specifically their scattering behavior. Neutrons are subatomic particles that have no electric charge, and they can interact with matter through various mechanisms, one of which is scattering. Scattering occurs when a neutron collides with an atomic nucleus or an electron in a material, and changes direction without being absorbed.
The question asks to calculate the macroscopic cross-section for scattering of neutrons in water at a specific energy of   . The macroscopic cross-section is a measure of how likely it is for a neutron to scatter in a given volume of material, and it is obtained by summing the product of the number density of each element in the material and its scattering cross-section. The scattering mean free path is then calculated as the inverse of the macroscopic cross-section, and it represents the average distance that a neutron travels in the material before scattering.
To solve the problem, the number density of hydrogen and oxygen in water is needed, as well as the respective scattering cross-sections for these elements. The problem provides these values, and the calculation is straightforward using the equation for the macroscopic cross-section and the definition of the scattering mean free path. This problem is relevant to nuclear engineering and radiation protection, as it is important to understand how neutrons interact with materials in order to design safe and efficient nuclear systems and to protect workers and the public from the effects of ionizing radiation.


The macroscopic cross-section for scattering of neutrons in water is given by the sum of the product of the number density of each element and its scattering cross-section: