Lecture 27
Nuclear Reactions
Chapter 29.5  29.8
Outline
• Radioactive Decay
• Binding Energy
• Nuclear Reactions
Half-Life
The half-life of a radionuclide is the period of time
needed for half of any its initial amount to decay.
Radionuclides have unchanging half-life.
This is the base for archaeological dating.
Half-life for 14C is 5730 years.
14
14 N + e + ¯
C

6
7
¯  antineutrino
Natural abundance ratio of 14C and 12C is ~ 1.31012
Creation of 14C is due to cosmic rays
After death, organisms stop absorbing 14C from the
atmosphere and the ratio decreases with time.
Half-Life
Problem with Carbon Isotopes
Problem: A 1-gram sample of wood is taken from
an ancient site. If the 14C activity of the sample is
12.5% that of the present-day organic material,
what is the age of the wood?
Solution: Half-time of 14C = 5730 years.
12.5% = 1/8 = 3 half-times of 14C.
The sample age is 3*5730 years ~ 17200 years.
Binding Energy
Hydrogen has 3 isotopes: protium, deuterium, and
tritium.
The mass of 11H is 1.0078 u , the mass of a neutron
is 1.0087 u . The sum is 2.0165 u .
The mass of a deuterium atom is 2.0141 u: 0.0024 u
= 2.2 MeV less than the combined mass of p+n.
All atoms have smaller masses than the sum of masses
of their nucleons.
Some mass and energy is given off due to action of
forces that hold the protons and neutrons together.
This energy is called binding energy.
Binding Energy
Binding energy of a deuterium atom is 2.2 MeV
(1.1 MeV per nucleon) ,
of a 20983Bi is 1640 MeV (7.8 MeV per nucleon).
A typical binding energy is ~800 billion kJ/kg
To boil water it takes 2260 kJ/kg
The most stable element is iron (5626Fe).
Problem with Binding Energy
What is the binding energy per nucleon of
Masses: 19779Au: 196.967 u
1 H : 1.0078
1
1 n : 1.0087
0
197
79Au?
1u = 931.5 MeV/c2
Solution: there are 79 p and 118 n in an Au atom.
mass(79p+118n) = 198.643 u
Difference between the actual mass and  = 1.676 u
E = mc2 = 1.676 u * 931.5 (MeV/u) /197 =
7.92MeV
Nuclear Reactions
Nuclear reactions are changes of elemental
composition in atomic interactions.
In chemical reactions atomic composition does
not change.
Elements lighter than Fe can be produced by fusion
of 2 smaller nuclei.
This is possible, because binding energy increases
with atomic number.
Fusion requires extremely high temperatures and
pressures  fusing nuclei come very close together
to overcome Coulomb repulsion forces.
Fusion
Fission
Fission is splitting of a large nucleus into a few
lighter nuclei.
It is possible for atoms heavier than Fe because
the binding energy decreases with the atomic
number.
Fission does not require extreme conditions and
could be easily controlled.
The first controlled fission reaction was achieved
in 1939 .
Fission animation
Summary
There are two basic types of nuclear reactions:
fusion and fission.
Fusion is creation heavier elements from lighter
ones. It works from hydrogen to iron.
Fission is a decay of heavy elements into lighter
parts. It works in elements heavier than iron.
Fusion is much more energy efficient than fission.