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knoximator
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ok, this is the question:
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?
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?
Last edited: