2 protons 2 neutrons
Energy of a nucleus
The
mass
of
a helium
nucleus is slightly
smaller
(<1%) than
the combined masses of its four nucleons.
This
mass difference is converted to energy via E=mc2.
Helium nucleus
6.695·10-27
kg 6.645·10-27
kg
Ch. 14
Conversion of mass to energy
5 ·10-29
kg
of mass is converted to energy when 2 protons and 2 neutrons are combined to form the helium nucleus:
E=mc2
= (5·10-29
kg) · (3·108
m/s)2 = 4.5
·10-12
J = 28
MeV
Each of the four nucleons releases 28 MeV
/ 4 = 7 MeV
1
J = 6.24
1018
eV
· 1H
4He
Energy per nucleon in MeV
Ni
Nucleon Number A
Energy per nucleon
Fe and Ni have are the most stable nuclei (lowest energy per nucleon).
Principle
of
nuclear
fusion
Energy is released when combining
two
light
nuclei
into one heavier nucleus.
Fusion vs. fission
•
Energy
is
released either by combining two small nuclei
(fusion)
or
by
split-
ting a large nucleus into two pieces
(fission).
•
The
energy
is
released as radiation and as kinetic energy. Both eventually turn into heat (the fire-
ball from a
nuclear
bomb and
the
steam
generated in a nuclear reactor).
Fe Ni
Pu
Pu
Plutonium
Nucleon Number A
Fusion vs. fission in bombs, reactors
•
Fusion
powers hydrogen bombs.Fission
powers atomic bombs.
•
Fusion
has not yet been tamed for peaceful purposes.Fission
generates energy in nuclear
reactors.
Fusion in stars
•
Stars convert hydrogen
to helium and heavier elements. When Fe and Ni are reached, fusion stops. The star has burnt its nuclear fuel and collapses
under its own gravity.
•
In massive stars, this collapse releases a huge amount of gravitational energy that leads to a supernova.The outer 90% of the star is ejected,
and the
center
becomes either
a black
hole
(>3 solar masses) or
a neutron star
(between 1.4 and 3 solar masses), where the atoms collapse into a
single huge nucleus. Lighter stars become white dwarfs .
•
All elements heavier than iron/nickel
are created during a supernova
explosion,
which has enough thermal energy
to form nuclei with higher energy per nucleon.
Stable nuclei
Red dots
=
stable nuclei.
The gray region contains unstable nuclei, created in the laboratory.
Stable nuclei have about equal
neutron
and
proton
numbers
NandZ (dashed).
At high Z, there are more neutrons
than
protons,
be-
cause
protons
are
charged and repel each other.
Radioactive decay
If the ratio of protons to neutrons gets too far off-balance,
a nucleus
will
spontaneously transform itself into another nucleus with a better ratio by
emitting
,
,
particles.
particle = 2p2n
= He nucleus
particle = electron
particle = photon
Marie Curie, Nobel prizes in
physics, chemistry
Isotopes
Isotopes are different
versions of the same element (same
Z).
They
have
the same number
of electrons and protons
, but a
different neutron number N.
Their
chemical
behavior is the same,
since
that
is
determined
by the electron number (=Z).
Stable isotopes are shown as red dots.The gray region con-
tains
unstable isotopes which are radioactive.
Different isotopes of the same element
Isotopes of hydrogen
Hydrogen Deuterium Tritium
One proton One proton one neutron
One proton two neutrons
These three isotopes play a central role in various fusion reactions.
Isotopes of carbon
•
Carbon
has 6
protons and 6
electrons
(Z=6). Its outer shell contains 4 electrons, which determine the chemical properties of carbon.
•
The most common isotope of carbon has 6 neutrons, 12 nucleons. It is commonly labeled 12C (“C twelve”).
•
14C is another isotope of
carbon containing 8 neutrons,
14 nucleons.
•
14C is unstable and decays radioactively.
The decay of 14C is exponential (Lect. 4, Slides 5,6). After 6000 years, half of the 14C has decayed
(= half-life).
After
another 6000 years,
one loses another half, and so on every 6000 years.
Half-life
Carbon-dating question
The 14C/12C ratio in a fossil bone is found to be ⅛
of the ratio in a living animal.
What is the approximate age
of
the
fossil?
A. 6
000 years
B.
18
000 yearsC.
32
000
years
D.
48
000
yearsSince the ratio has been reduced by a factor of ⅛
= ½½½ = (½)3,
three half-lives have passed, i.e.
3 ·
6000 years = 18
000 years
•
Radioactive 14C is created
continuously by cosmic
rays (next slide).
•
14C oxidizes to CO2
and is converted by plants into organic matter. Particularly durable are wood and charcoal generated from wood.
•
Animals and humans eat plants and incorporate
14C into the bones.
•
Decaying 14C is replenished as long as plants and animals are alive.
•
Once a plant or animal dies, its 14C content decreases and thereby starts the clock for radiocarbon dating.
•
By measuring the 14C/12C ratio of a sample from an archaeological site one can determine its age. (Willard Libby, 1969 Nobel Prize)
•
This can be done up to an age of about
60
000 years,
when the
14C concentration has been reduced by a factor of (½)10
=
1/1024 .
Radioactive dating
Production of carbon 14C
A cosmic ray proton shatters the nucleus of an atom in the upper atmosphere,
creating neutrons n plus other debris.
A 14N nucleus
absorbs a neutron and
emits a
proton,
becoming
14C.
Concentration of 14C
•
A balance between the
production and decay rates determines the equilibrium ratio:
•
Such an extremely low ratio of one part in a trillion requires a
very sensitive detector which can detect single 14C atoms.
•
It helps to have a large number of C atoms from a macroscopic sample (compare Avogadro’s number, 1024).
14 C12C
1.31012
•
For older specimens one uses isotopes with longer half-life, for example 235U (uranium). Its half-life is 0.7 billion years.
•
The oldest rocks on Earth have been dated this way. These are 4.4 billion years old.
•
A
focused
ion
beam
removes
a
small
amount
of
material
from several spots on one of the tiny red zircon crystals.
Geological dating
