# Neutron energy after one elastic collision

1. May 4, 2012

### knoximator

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=$\frac{1}{ζ}$*ln$\frac{E_{0}}{E_{n}}$
n= number of collisions
ζ=depends on atomic mass of target≈ $\frac{2}{A+\frac{2}{3}}$ (A= atomic mass)
for A=1, ζ=1!
$E_{0}$= original energy of neutron before collision
$E_{n}$= energy of neutron after n collisions

so, inputting n=1, i get the equation $E_{1}$=$E_{0}$*$e^{-ζ}$

and subsequently, i get the following energies:

a. $E_{1}$=0.367*$E_{0}$
b. $E_{1}$=0.472*$E_{0}$
c. $E_{1}$=0.0853*$E_{0}$
d. $E_{1}$=0.9916*$E_{0}$

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: $\frac{σ_{s}(E)}{σ_{t}(E)}$ 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: May 4, 2012
2. May 4, 2012