ok, this is the question:(adsbygoogle = window.adsbygoogle || []).push({});

neutrons scatter elastically at 1.0MeV. after one scattering collision, determine what fraction of neutrons will have energy of less than 0.5 MeV if they scatter from:

a. hydrogen

b. Deuterium

c. Carbon-12

d. Uranium-238

solution process...

the basic equation to be used: n=[itex]\frac{1}{ζ}[/itex]*ln[itex]\frac{E_{0}}{E_{n}}[/itex]

n= number of collisions

ζ=depends on atomic mass of target≈ [itex]\frac{2}{A+\frac{2}{3}}[/itex] (A= atomic mass)

for A=1, ζ=1!

[itex]E_{0}[/itex]= original energy of neutron before collision

[itex]E_{n}[/itex]= energy of neutron after n collisions

so, inputting n=1, i get the equation [itex]E_{1}[/itex]=[itex]E_{0}[/itex]*[itex]e^{-ζ}[/itex]

and subsequently, i get the following energies:

a. [itex]E_{1}[/itex]=0.367*[itex]E_{0}[/itex]

b. [itex]E_{1}[/itex]=0.472*[itex]E_{0}[/itex]

c. [itex]E_{1}[/itex]=0.0853*[itex]E_{0}[/itex]

d. [itex]E_{1}[/itex]=0.9916*[itex]E_{0}[/itex]

and that is where i get stuck, i have no clue on how to continue and get a fraction out of the information i got.

in the book, there's a probability equation presented, but i can't see any use of it to my question

Edit

ok, so after some deep book delving session, i might have found my problem.

basically, i don't think i need the equation above, but should rely more on the neutron cross section σ tables for the elements mention above and the specific energies.

for example: [itex]\frac{σ_{s}(E)}{σ_{t}(E)}[/itex] is the probability of a neutron to scatter for a certain energy E

my question is, how to use this relation, and which energies to use?

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# Neutron energy after one elastic collision

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