Nuclear Reactions
& Applications
Nuclear Reactions
•  Nuclear Reactions:
x+X!y+Y
or X(x,y)Y
Q = (Initial Mass) c2 – (Final Mass) c2
= (Mxc2+MXc2) – (Myc2+MYc2)
Example:
α + 14N ! p + 17O
or 14N(α,p)17O
Q = (Initial Mass) c2 – (Final Mass) c2
= (Mαc2+M14Oc2) – (Mpc2+M17Oc2)
[Can be generalized to any (low energy) reactions: X1+X2 ! Y1+Y2+Y3+…]
(Spontaneous) Fission
Some heavy isotopes can fission spontaneously into
two so-called “fission fragments” (+ possibly some
neutrons…)
Ex: 256Fm (t1/2=2.6 h)
254Cf (t =60.5 days)
1/2
The fission fragments are statistically distributed over
a large range of medium-mass nuclei and are usually
radioactive (and β-decay back to stability)
! How fast depends of the half-lives of
the isotopes formed on the way !
Induced Fission
Because the neutron has no charge, it can
penetrate the nucleus (no Coulomb barrier)
! Neutron used as a Probe.
Example:
1938-39: Induced fission of 238U
! large release of energy (~200 MeV)
! new neutrons are emitted !!!
! CHAIN REACTION POSSIBLE ?
Leo Szilard
Thermal Neutron Mechanism
•  Fission fragments are highly unstable because they
are so neutron rich.
•  Prompt neutrons are emitted simultaneously with the
fissioning process. Even after prompt neutrons are
released, the fission fragments undergo beta decay,
releasing more energy.
•  Most of the ~200 MeV released in fission goes to the
kinetic energy of the fission products, but the
neutrons, beta particles, neutrinos, and gamma rays
typically carry away 30–40 MeV of the kinetic energy.
U-235 Fission Cross Section
Faster Neutrons
Chain Reaction
•  More than one neutron (on average) is emitted after every fission:
possibility of triggering a chain reaction.
•  Neutrons emitted are “fast neutrons”, need to be slowed down
(“slow/thermal neutrons”). [Fission cross sections increases by 1/v]
•  Chain Reactions:
–  Slightly more than one neutron emitted per reaction ! chain reaction
critical
–  Less than one neutron ! subcritical
–  More than one neutron ! supercritical
Applications of induced fission
Controlled:
Nuclear Power Plant
Waste: long-lived fission fragments
(ex: 90Sr, 137Cs…)
Uncontrolled:
Atomic Bomb (A-bomb)
Hiroshima:
Energy released 1014 Joules = 20 kilotons of TNT
Nasty stuff (after blast): fission fragments !
Reading: “The making of the Atomic Bomb” (Richard Rhodes)
Nuclear Reactor
Core:
Moderator [hydrogen in water, beryllium, carbon in graphite]:
! slows down the neutrons to “thermal” energies
Control rods [Boron for example]
! absorbs the neutron excess, control the criticality of the reactor
Reflector [hydrogen in water]
! allows backscattering of the neutrons back in the cells.
Power Plants
Example:
Fusion
Fusion releases more energy per
nucleon than fission. However, this
process doesn’t occur spontaneously.
One needs to ignite the reaction, then
the energy produced has to self-sustain
the fusion process.
That’s what is happening in the Sun:
4 1H ! (several steps) !4He, Q=26.7 MeV
(then: 3 4He ! 12C, etc…)
Applications to induced fusion
Controlled:
Nuclear Fusion Power Plant
(projects: tokamaks, laser…)
New initiative: ITER project
Problem: Ignition !
Uncontrolled:
Hydrogen Bomb (H-bomb)
requires an A-bomb to ignite fusion !!!
Enhanced yield:
Hundreds of kilotons ! Tens of Megatons !
(Hiroshima, 20 kt)
Reading: “Dark Sun” (Richard Rhodes)
(Ivy) Mike – Oct
Device: 60 tons, Yield: 10.4 MT
st
31 ,
1952
Castle Bravo
Expected Yield: 4-8 MT
Measured Yield: 15MT !!!
First lithium-deuteride “dry” bomb:
40%: 6Li ! d, t, n…
60%: 7Li + n ! 6Li + 2n (Oops!!!)
A fusion reactor ?
Inertial Confinement
Application: Oil & Mining
Neutron sources: PuBe or AmBe sources
Many more applications
•  Archeology: 14C (t1/2 ~ 5730 years)
•  Medicine: X-rays, radioactive tracers (ex:
…) + imagery, radiotherapy
99m
Tc,
•  Engineering: γ-radiography of material, neutron
activation, thickness control…
•  Other applications: Smoke detector,
Sterilization, …
Carbon-14 Dating
14C
is a radioactive isotope of carbon with a half-life of t1/2=5730y. It is produced in
our atmosphere by the bombardment of 14N by neutrons (produced by cosmic rays).
1. Write the reaction that produces 14C.
14C
can be absorbed by a living organism the same way than the stable carbon
isotope 12C. The equilibrium ratio R0 = N(14C)/N(12C) in the atmosphere has been
measured to be 1.20x10-12. When an organism dies, it ceases absorbing carbon
(both 12C and radioactive 14C) and therefore the ratio R(t) changes over time as 14C
nuclei decay.
Application: a bone suspected to have originated during the period of the roman
emperors was found in Great Britain. The N(14C)/N(12C) ratio was determined to be
1.10x10-12.
2. Write the radioactive decay law for the 14C nuclei. Express the decay law
using R(t) and R0.
3. How old is the bone according to the 14C dating method? Is the bone old
enough to have Roman origins?
99mTc
– T1/2=6.01h
Metastasis
Radiotherapy
Radiotherapy delivered internally
Radiotherapy delivered externally
CAT scan
Computer Assisted
Tomography