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Moderating a Neutron In a nuclear reactor, neutrons
Chapter 9, Problem 40P(choose chapter or problem)
Problem 40P
Moderating a Neutron In a nuclear reactor, neutrons released by nuclear fission must be slowed down before they can trigger additional reactions in other nuclei. To see what sort of material is most effective in slowing (or moderating) a neutron, calculate the ratio of a neutron's final kinetic energy to its initial kinetic energy, Kf/Ki, for a head-on elastic collision with each of the following stationary target particles. (Note: The mass of a neutron is m = 1.009 u, where the atomic mass unit, u, is defined as follows: 1 u = 1.66 × 10−27 kg.) (a) An electron (M = 5.49 × 10−4 u). (b) A proton (M = 1.007 u). (c) The nucleus of a lead atom (M = 207.2 u).
Questions & Answers
QUESTION:
Problem 40P
Moderating a Neutron In a nuclear reactor, neutrons released by nuclear fission must be slowed down before they can trigger additional reactions in other nuclei. To see what sort of material is most effective in slowing (or moderating) a neutron, calculate the ratio of a neutron's final kinetic energy to its initial kinetic energy, Kf/Ki, for a head-on elastic collision with each of the following stationary target particles. (Note: The mass of a neutron is m = 1.009 u, where the atomic mass unit, u, is defined as follows: 1 u = 1.66 × 10−27 kg.) (a) An electron (M = 5.49 × 10−4 u). (b) A proton (M = 1.007 u). (c) The nucleus of a lead atom (M = 207.2 u).
ANSWER:
a.)
Step 1 of 3
We have to calculate the ratio of neutron's final kinetic energy to its initial kinetic energy,
for a head-on elastic collision with an electron.
The ratio of neutron's final kinetic energy to its initial kinetic energy is
Where,
and
are the initial and final speed of the neutron
after a head on collision with an electron
mass of the neutron
Now, since the electron is at rest, the final speed of the neutron after colliding with it can be found using the equation
where,
mass of a neutron = 1.009 u
mass of an electron =
u
Hence, the ratio of is
.
=
= 0.9978
Therefore, the ratio of neutron's final kinetic energy to its initial kinetic energy,
for a head-on elastic collision with an electron is 0.9978 .
b.)