Quanta to Quarks
Focus Area 3
The Nucleus
Typically the nucleus is less than
one ten-thousandth the size of
the atom, the nucleus contains
more that 99.9% of the mass of
the atom.
Nuclei consist of positively
charged protons and electrically
neutral neutrons held together by
the so called strong nuclear force.
This force is much stronger than
the repulsive electrostatic
(Coulomb) force, but its range is
limited to distances on the order
of a few (10-15) metres.
The number of protons in the nucleus, Z, is called the atomic number. This
determines what chemical element the atom is.
The letter N denotes the number of neutrons in the nucleus. The atomic
mass of the nucleus,
A=Z+N
and gives the total number of nuclear particles in the nucleus which are
collectively referred to as nucleons.
Protons carry a charge of 1.602 × 10-19C. Neutrons carry no charge. Protons
have a mass of 1.672 × 10-27 kg. Neutrons are slightly more massive with a
mass of 1.675 × 10-27 kg.
Wait…when did they find the neutron?
As early as 1907 it had been suggested that
protons alone were not sufficient to account for
the mass of most atoms.
It was suspected that there must be another
nucleon, with considerable mass, but no electric
charge.
The existence of the neutron was proven in 1932
by James Chadwick (1891-1974).
It was impossible then to detect and measure
neutrons directly.
The method Chadwick used relied upon neutrons
colliding with other particles, then applying the
scientific principles of Conservation of Energy
and Conservation of Momentum to measure the
properties of the neutron.
In 1920, Rutherford guessed that there had to
be a new kind of particle in the nucleus,
about as heavy as a proton but with no
electric charge, which he called the neutron.
Others thought that whatever it was in the
nucleus might be high energy gamma ray
photons (radiation had been discovered by
then).
In 1932, Frederic & Irene Joliot (Irene was the
daughter of Marie Curie) fired alpha particles
(helium nuclei) at beryllium and it was seen
that the beryllium ejected something from
the nucleus that caused paraffin to release
protons.
Whatever it was could pass through thick
sheets of lead, but they were stopped by
water or paraffin wax.
Since large numbers of very energetic protons were emitted
from the paraffin when it absorbed whatever was coming out of
the nucleus, they assumed that whatever was being ejected from
the beryllium nuclei must be an extremely energetic form of
gamma radiation. Chadwick, however, disagreed.
Chadwick showed that whatever was ejected from the beryllium
nuclei could not be radiation because it did not have sufficient
energy to then eject protons from paraffin wax. Whatever it was
that could knock protons out of other atoms had to be a fairly
heavy particle, not a massless particle such as gamma radiation.
Another result that suggested that the unknown radiation was
not gamma rays is that they did not discharge a charged
electroscope, whereas gamma rays do discharge a charged
electroscope due to the photoelectric effect.
Using the velocity of the ejected protons and the laws of
conservation of energy and momentum, Chadwick
calculated the mass of the unknown particle. It was just a
little heavier than the proton. He had no doubt that this
was Rutherford's neutron.
Chadwick explained the process occurring in the
experiment as:
Chadwick explained that when the neutrons emitted from
the beryllium collided with the light hydrogen nuclei in
the paraffin, the neutron came to a sudden stop and the
hydrogen nucleus (proton) moved off with the same
momentum as the neutron had before the collision.
Radioactivity
Henri Becquerel discovered
radioactivity in 1896.
Ernest Rutherford studied this new
phenomenon and found that there
were two different types of radiation
that could be emitted from
radioactive elements.
To distinguish between them he
called them alpha and beta radiation.
When Paul Villard found a third type
of radiation in 1900, Rutherford called
it gamma radiation.
Transmutation
Rutherford and Frederick Soddy
discovered that atoms change
from one element to another as a
result of emitting radiation.
This is called transmutation.
Transmutation is a nuclear
reaction where the structure of
the nucleus changes, emitting
particles or a gamma ray in the
process.
Rutherford received the Nobel
Prize in Chemistry in 1908 for this
work.
Alpha Decay
Alpha decay occurs in atoms which have a very large
nucleus and are unstable. To achieve greater stability,
the nucleus may spontaneously eject an alpha
particle to carry away excess mass and energy.
Beta Decay
Some atomic nuclei, of any size, have an unstable mix of
protons and neutrons. If there is an excess of neutrons, a
neutron can be turned into a proton plus an electron.
The result is that: Number of neutrons decreases by 1,
Number of protons increases by 1. (This means Atomic
Number goes up by 1 but Atomic Mass Number does not
change), The electron is ejected from the nucleus at high
speed. This is the Beta particle... a high speed electron.
When a nucleus ejects a positron ( ) as a result of
beta decay, its atomic number will decrease by 1 but
its mass number will remain unchanged. In this case,
a neutrino (ν) will also be ejected. A neutrino also has
no charge and little mass.
This is called beta plus (β+) decay. The positron is
produced when a proton changes into a neutron. The
positron carries away the excess charge, as shown
below.
The general equation for β+ decay is shown below:
Line of Stability
Nuclides that are above the
line of stability tend to move
closer to it by releasing an α
particle.
Nuclides that are to the left
of the line of stability (i.e.
contain too many neutrons)
tend to move toward
stability using β- decay.
Nuclides that are to the right
of the line of stability tend
to undergo β+ decay in
order to become more
stable.
Gamma Radiation
Gamma (γ) rays are high frequency electromagnetic
waves that carry away excess energy from unstable
nuclei. The unstable nuclei are shown by the letter
‘m’ (for metastable) after the mass number, or by an
asterisk after the element symbol.
The parent nucleus is usually unstable because it was
formed as a result of α or β decay. Therefore, γ decay
usually follows α or β decay. This may happen
immediately, or some time later.
Jimmy Neutrino
The neutrino was first
postulated in 1930 by
Wolfgang Pauli to preserve
the laws conservation of
energy and momentum in
beta decay.
He theorized that an
undetected particle was
carrying away the observed
difference between the
energy and momentum of
the initial and final particles
in beta decay.
Pauli originally named his
proposed light particle a
neutron.
When James Chadwick
discovered a much more
massive nuclear particle in 1932
and also named it a neutron,
this left the two particles with
the same name.
Enrico Fermi, who developed
the theory of beta decay,
coined the term neutrino in
1934 as a way to resolve the
confusion.
It is the Italian equivalent of
"little neutral one".
During decay it was found that beta particles could have a range of
kinetic energies rather than one specific energy as in alpha decay.
It was proposed that the total energy lost by the nucleus during
decay was shared by the neutrino and the electron being ejected.
Since the kinetic energy of the electron varied, there must be
another particle whose kinetic energy could also vary so that the
sum of their energies was always the same.
The simultaneous emission of a beta
particle and a neutrino in beta decay
allowed for energy and momentum to be
conserved.
This theory was accepted for almost a
quarter of a century without any direct
evidence to support it. In 1956, an
experiment was performed in a nuclear
reactor that could only occur if the
neutrino actually existed, thus confirming
its existence.
Fermi’s Firm Findings
After the discovery of the neutron which was large and uncharged, Enrico Fermi
tried to extend the number of known elements through transmutation.
In 1934 he bombarded uranium-235 with neutrons expecting that the uranium
would take up the neutron and then it would undergo beta decay to produce an
isotope of neptunium as shown in the equation below.
Two lighter nuclei were actually produced as fission products in an artificial
transmutation as shown in the equation below.
Fermi has actually succeeded in producing the first artificial transmutation using
nuclear fission - when heavier nuclei are split into two or more lighter nuclei.
Large nuclei are unstable because protons at the surface of the
nucleus are repelled by a force proportional to the total
number of protons in the nucleus, but attracted towards the
interior by a force proportional to the number of nucleons in its
immediate vicinity (which is constant for light or heavy nuclei).
Thus the electrical repulsion sets a maximum limit to the
number of protons in a nucleus.
The maximum limit to the number of neutrons is set by the
strong nuclear force that seeks to bind pairs of neutrons to
pairs of protons.
Thus if the neutron excess becomes too large, a neutron
spontaneously changes into a proton.
Since very heavy nuclei have too many of both neutrons and
protons, they spontaneously emit tightly bound nuclear sub
assemblies. This is naturally occurring fission or transmutation.
Fission or transmutation may be artificially triggered by bombardment with
neutrons.
Heavy nuclei break up under such bombardment into a pair of lighter nuclei with
the release of energy far exceeding the total kinetic energy of the colliding
particles. This excess energy is due to the reduction of nuclear mass. As stated,
some nuclei can be made unstable by firing an extra neutron into them.
This is called a fission reaction because the nuclei split into two fragments. When the
nucleus decays, more neutrons are ejected. If these neutrons cause further fissions to
occur a chain reaction occurs.
At each step of this process, mass is
converted into energy which is released as
the kinetic energy of the particles in the
system. Controlled chain reactions produce
enormous amounts of energy this way and
they take place in nuclear reactors, which use
a fissionable material such as uranium-235.
Forces
What holds the nucleus together?
This question had been asked as soon as Rutherford had proposed
that atoms have a nucleus. There were just 2 forces then
understood, which could be operating in the nucleus.
Gravity: All masses attract all other masses by gravity. This would
attract all nucleons to each other.
Electrostatic Forces: All charged particles exert a force on other
charged particles. This force would not act on neutrons, but should
cause protons to be repelled by other protons.
Calculations showed that the electrostatic repulsion would be
much, much stronger than gravity. The nucleus should instantly fly
apart!
Someone has a STRONG
feeling about this
Since the nucleus does exist, and doesn’t instantly explode, it
was realized that there must be another force operating.
It was called simply the “Strong Nuclear Force”. Its properties
could be inferred and calculated:
• It must be much stronger than the proton proton electrostatic
repulsion. (it’s over 100X stronger)
• It must be independent of charge and attract all nucleons...
protons & neutrons.
• It must be extremely short-ranged, operating only across the tiny
distances of the nucleus. (Otherwise it might cause neighbouring
atomic nuclei to fuse together, and eventually pull all matter into
one lump!)
The “atomic mass unit” (u) is a measure of mass
devised for convenience in Chemistry. Roughly
speaking, both a proton and a neutron have a mass of
1 u, although in the calculations following, you need
to be much more precise.
Obviously, 1 u is a very small mass:
1 u = 1.661x10-27 kg
You need to be able carry out calculations using
either unit, so the following data may be useful.
The “electron-volt” (eV) is an energy unit that is
convenient because the energy of sub-atomic particles has
traditionally been measured by their behaviour within
electric fields. 1 eV is the energy gained by an electron
accelerating in an electric field with a potential difference
of 1 volt. 1 eV is an extremely small amount of energy:
1 eV = 1.602 x 10-19 joules of energy
so the unit often used is the mega-electron-volt (MeV)
1 MeV = 1x106 (one million) eV
This is convenient when dealing with individual atoms or
particles.
There is something defective here
It was realized that incredibly powerful forces were operating within the
atomic nucleus. How could such forces arise?
The answer lies in the fact that the mass of every atomic nucleus (except
hydrogen ) DOES NOT ADD UP.
An alpha particle or helium nucleus has a mass of 4.00150 u. If we were to
add the masses of two protons and two neutrons we would get a mass of
4.03190 u for an alpha particle.
The sum of the inidividual masses of the protons and neutrons is 0.03040 u
larger than the sum of the alpha particle as a whole.
This difference in mass is known as the mass defect and it represents the
mass lost when a nucleus is assembled from its constituent parts.
As you would expect, the mass lost in assembling the nucleus is converted
to energy and this energy is used to bind the nucleus together.
In a bind
We could convert the mass from atomic mass units to kilograms
and then use ΔE=Δmc2 to calculate the energy used to bind the
nucleus together in joules.
But these numbers are not convenient so instead we calculate
the energy in electronvolts using the mass in atomic mass units.
Since 1 u is equivalent to 931.5 MeV/c2 we can calculate the
binding energy as follows:
ΔE = Δmc2 = 0.03040 x 931.5 = 28.3 MeV
The binding energy of a particular nucleus will depend the total
number of nucleons in the nucleus so large nuclei will have
higher binding energies.
To make standardised comparisons between light and heavy
nuclei we use a standard called the binding energy per nucleon.
For the helium nucleus above the binding energy per nucelon
would be 28.3 / 4 = 7.075 MeV.
Fermi’s Demo
Fermi achieved the first artificially produced nuclear fission in
1934. He was able to irradiate unranium-235 with slow
neutrons and produce a radioactive product that produced
alpha particles.
He incorrectly assumed that this product was an isotope of
neptunium (atomic number 93) but later the products were
discovered to be the lighter elements of bromine and
lanthanum.
Fermi in 1939, escaped to the United States where he
continued his research into fission. Delayed by economic
and security constraints, he secretly build Chicago Pile 1, the
world’s first nuclear fission reactor in 1942.
Having theoretically calculated that fission was possible
from naturally occurring uranium, he set about construction
of a pile of graphite blocks to slow or moderate the speed
at which the neutrons would travel.
He used cadmium control rods to absorb neutrons and
control the rate of reaction. This demonstration of a
controlled nuclear fission reaction started an accelerated
program by the US army to develop a nuclear bomb, the
Manhattan Project.
Controlled & Uncontrolled Nuclear Reaction Chains
Homework:
Compare Controlled & Uncontrolled Nuclear Reaction
Chains.
Due: On Edutone by tomorrow
Wilson Cloud Chamber
http://youtu.be/NeydrHKvpYM
End of FA3