Nuclear PhysicsATOMIC, NUKE & QUANTUM NUCLEAR PHYSICSExplain
how the radii of nuclei can be determined by charged particle
scattering experiments.Use of energy conservation for determining
closest-approach distances for Coulomb scattering experiments is
sufficient.Essentially we toss charged particles towards a nucleus
and measure what angles they come off and at and then calculate
backwards how close they must have been to the nucleus Since the
nucleus is positively charged it will exert a force on the charged
particle and thus alter its trajectory. Often the mass of the
nucleus is much larger than that of the charged particle so when
the charged particle collides the change in momentum of the nucleus
can be ignored. Thus the particle goes in with a known amount of
kinetic energy and will come out with the same amount of kinetic
energy. As the charged particle gets close to the nucleus the
electric potential energy of the charged particle will change. The
math is not particularly simple, but using some fancy algebra and
conservation of energy we can calculate the distance of closest
approach. If we keep giving the particle more energy we can get
closer and closer thus getting better approximations of the size of
the nucleus. Check outhyperphysicsfor a more complete discussion
and a derivation.Describe how the masses of nuclei can be
determined using a mass spectrometer.Students should be able to
draw a schematic diagram of the mass spectrometer but the
experimental details are not required. Students should appreciate
that nuclear mass values provided evidence for the existence of
isotopes.
Isotopes of a given element differ only by the number of
neutrons in the nucleus. Thus different nuclides have different
masses. Therefore we should be able to sort the isotopes by their
massThis is done using what is called a mass spectrometer. First
the atoms are ionized so that they have a net electric charge. This
allows us to do a couple of things.Picture Stolen
from:http://en.wikipedia.org/wiki/Mass_spectrometryFirst it allows
us to accelerate the ions using an electric potential. The ions
then pass through a uniform magnetic field, that is perpendicular
to the path of the ions.In the picture above the magnetic field
would be perpendicular to the page.Since the ions are charged and
moving relative to the magnetic field they feel a tug. The tug
moves then in a circular path. The more massive the ion the less it
accelerates and the large its circular path. The less massive an
ion is the more it accelerates and the smaller its circular path.
Thus the isotopes have been separated by mass.The force on the ions
is:(1)F=qvBWhereqis the charge of the ion,vis the velocity of the
ion andBis the strength of the magnetic field. Then using Newtons
2nd law:(2)F=maCombining the two:(3)ma=qvBWe find that the mass
is:(4)m=qvBaWhere the acceleration is centripetal and given by the
following equation:(5)a=v2rWhere v is the velocity of the particle
and r is the radius of the circular path. Thus the mass
is:(6)m=qBrvIts worth noting that the mass spectrometer actually
measures the mass to charge ratio, not just the mass, however if
you are dealing with atoms of the same element they will all have
the same charge when ionized and thus you are effectively measuring
the mass.Describe one piece of evidence for the existence of
nuclear energy levels.When radioactive nuclei decay by gamma decay
the energies of the gamma rays is distinctive of the nuclei. As the
nucleus de-excites is does so very much in the same way that an
electron around an atom de-excites. The nucleus has orbitals and
energy levels, so when it drops from one energy level to a lower
energy level energy is released in the form of a gamma ray (high
energy photon). The energy of the gamma ray is equal to the energy
different between the two nuclear energy levels.(7)E=E2E1Describe
both+anddecay, including the existence of the neutrino and the
antineutrino.Students should know thatenergy spectra are continuous
and that the neutrino was postulated to account for the missing
energy and momentum.Beta Decay There are two types of beta decay,
positive and negative. Positive beta decay is the process by which
a neutron decay into a proton and an electron. The neutron is made
of three quarks, one up quark and two down quarks. One of the down
quarks is converted to an up quark by the emission of a W boson
thus the quark changes flavor. Beta decay is governed by the weak
nuclear force. The electron does not have enough energy to escape
the pull of the positively charged nucleus (protons), so the
electron must quantum mechanically tunnel out of the nucleus, that
is it borrows energy to jump outside the nucleus then returns the
energy and travels away from the nucleus with its initial energy.
The emission of the electron is also accompanied by the emission of
anti-electron-neutrino. Negative beta decay is given by the
following equation:(8)10n11p+01e+eNegative beta decay is the
process by which a proton decays into a neutron and a positron and
emits a electron neutrino. The mass of the neutron is greater than
the mass of the proton. Therefore negative beta decay does not
happen without an input of energy, the binding energy is lower in
the original nucleus.(9)energy+11p10n+0+1e+eBeta particles are
emitted at close to the speed of light and thus have a much great
penetration ability and therefore more hazardous to humans, they
have less ionizing energy than alpha particles.Unlike gamma decay
beta particles are given how in a spectrum of energies. For example
given a stationary nucleus (zero momentum and zero kinetic energy)
that undergoes beta decay. In order to conserve momentum and energy
the beta particle and the nucleus must both move away from one
another. However some of the energy and momentum is shared with a
neutrino, the energy is given out randomly to the 3 particles, only
obeying conservation of energy and momentum (conservation of
mass-energy). Thus the energy of the beta particle is not discrete
or characteristic of the nucleus.State the radioactive decay law as
an exponential function and define the decay constant.Derive the
relationship between the decay constant and half-life.Radioactive
decay is a random process, however if large numbers of nuclei are
involved patterns, trends or averages can be found. It is found
that the number of decays reduce exponentially with time. The
half-life is the amount of time for half of the original unstable
nuclei to decay. If there is originally N0 radioactive nuclei then
after one half-life , there will be N0 after two half-lives there
will be N0. The number of nuclei left is described by the following
equation:(10)N=N0(12)tT12=N02tT12Doing a little
math:(11)NN0=2tT12(12)log2(NN0)=tT12Then changing
base:(13)ln(NN0)ln(2)=tT12(14)ln(NN0)=tln(2)T12(15)N=N0etln(2)T12Where
we now define the following as the decay
constant:(16)=ln(2)T12=0.693T12Therefore the equation for
radioactive decay is:(17)N=N0etThis can also be rewritten in terms
of the activity:(18)A=A0etWhere A is the number of decays per
second and A0 is the number of decays per second at t = 0.Solve
problems using radioactive decay law.Example:Plutonium 239 has a
half life of approximately 24,400 years. Suppose a sample of Nuclei
and an initial activity of 4 mCi. Where 1 Curie (Ci) is the
activity of a radioactive material that decays at the rate of
disintegrations per second. Tippens, 6th Edition, page 880a) After
73,200 years how many of the nuclei are left?b) What is the
activity of the source after 73,200 years?SolutionGee I hope theyre
all that hard.Outline methods for measuring the half-life of an
isotope.Students should know the principles of measurement for both
long and short half-lives.If you want to measure the half-life of
substance the method is to stick a sample in front of a detector
and count the number of decays. Over a period of time the number of
decays will decrease and thus a plot of decays vs. time will
produce a nice exponential curve. The half-life can be calculated
from the decay curve. However a problem arises if the half-life is
very short or very long.Long half-lives:If the activity of a sample
is so small it may be difficult to measure a significant number of
decays in order to generate a decay curve. If a large amount of
radioactive substance is used then a significant number of decays
will occur per unit time, the activity can be measured. The decays
can then be detected. The detectors are never 100% efficient, so
the efficiency of the detector must be found using a source of
known activity. The activity is given by the following
equation:(23)A=Nt=NWhereNis the change in the number of radioactive
nuclei, is the change in time, N is the number of radioactive
nuclei in the sample and is the decay constant which is related to
the half life and thus what we want to measure. So the half-life
is:(24)T12=ln(2)(25)T12=ln(2)(AN)Short half-lives:Some nuclei have
such sort half-lives that transporting the sample to a detector is
virtually impossible, i.e. the substance decays before you get it
to the detector. In such cases the sample must be created
(Artificial Transmutation) in or very near a detector. (Gee, I
wonder if someone got a Nobel Prize of thinking of that
solution?)Nuclear Reactions Fission And FusionATOMIC, NUKE &
QUANTUM NUCLEAR REACTIONS FISSION AND FUSIONDescribe and give an
example of artificial (induced) transmutationConstruct and complete
nuclear reaction equationsArtificial transmutation is the changing
or manipulation of a nucleus artificially. The nuclear reaction
equation below is an example of artificial transmutation:
Nitrogen is bombarded with alpha particles (helium) resulting in
the creation of oxygen and hydrogen. The alpha particle is absorbed
by the nitrogen and a proton (hydrogen w/o an electron) is
released. This happened because someone set it up, thus its
artificial, and the nitrogen transmutated into oxygen.Another
example of a nuclear reaction is the Fission of Uranium-235 by a
slow (thermal) neutron:
Uranium-235 absorbs a neutron becomes Uranium-236 which is very
unstable and quickly breaks down into Strontium and Xeon. This is
one of several possible fission reacts, all Uranium fission uses
U-235 to create U-236, however the products are not always the same
(as with everything quantum-like there are probabilities dictating
the outcome).It is important to note that there are three
conservation laws that apply to nuclear reactions:1. The number of
nucleons in a nuclear reaction is conserved.2. The charge is
conserved, or the sum of the charges on the left is equal to the
sum of the charges on the right.3. The mass energy is conserved,
more on that laterDefine the term unified mass unitState and apply
Einsteins mass-energy equivalence relationshipExplain the concepts
of mass defect and binding energySolve problems involving mass
defect and binding energiesThe proton and neutron have very nearly
equal mass, albeit very small, approximately . This is not a very
convenient number, so a new unit was defined the atomic mass unit,
or as the IB likes to call it the unified mass unit,u. One unified
mass unit is defined as one-twelfth the mass of a carbon-12 atom.
Carbon-12 has 6 protons and 6
neutrons.(1)1u=massofonecarbon12atom12This is call an atomic mass
unit by Americans, I guess British or the IB likes to be different,
who cares. A unified mass unit (u) is defined to be the mass of
exactly one-twelfth of a carbon-12 atom. That works out to
be:(2)1u=1.661027kgSince the neutron and proton have approximately
the same mass, a proton and neutron have approximately masss of
approximately 1u.In the IB formula book:ParticleMass (u)
Electron (me)0.000549
Proton (mp)1.007277
Neutron (mn)1.008665
Helium Atom4.002602
If the math is done it can be seen that the helium atom weighs
less than the mass of two protons and two neutrons! The same can be
found with Oxygen that weighs 15.994915u, if fact it can be found
for all atoms. The difference between the mass of an atom and the
sum of an atoms parts is called the mass defect.The mass defect can
be explained by Einsteins mass-energy equivalence:(3)E=mc2If you
slam to small nuclei into each other and create a bigger atom (but
with less mass) then energy is released. The loss of mass is equal
to the energy released. For example:
It will take energy to break the new nucleus apart, the energy
required to break up a nucleus into in neutron and protons is
called the binding energy. In the reaction shown above the energy
required to reverse the reaction (break up the helium into
hydrogen) is equal to the energy released.The binding energy of an
atom can be approximated summing the mass of the individual
neutrons and the mass of the individual protons subtracting the
mass of the atom and multiplying by the speed of light
squared:(4)E=[Nmn+Zmpmassofatom]c2Where N is the number of
neutrons, mn the mass of a neutron (u), Z is the number and
protons, mp is the mass of a proton (u) and c is the speed of light
in MeVu-1.Describe the processes of nuclear fission and
fusionThings go boom.The nuclear fission is the process in which a
large nucleus splits into two or more smaller nuclei. The only
naturally occurring fissionable nucleus is Uranium 235. The Uranium
235 is bombarded with slow or thermal neutrons, the Uranium 235
captures a neutron and becomes Uranium 236 but it is an excited
Uranium 236, which is very unstable. The Uranium 236 nucleus
quickly decays by fission and splits into two nuclei. If the
Uranium 236 atom is allowed to settle to its ground state it will
be very stable and has a half of approximately 25 million years. An
example of the nuclear equation for the fission of Uranium 235 is
shown below:
The products of the nuclear reaction are not always the same.
There are several possible by products of the fission of Uranium
235.Note that in the reaction shown there are 2 neutrons released.
If these two neutrons are captured by other Uranium 235 nuclei two
more reactions occur and then there are 4 neutrons are released a
chain reaction occurs. This is how nuclear reactor stay on. If the
reaction is uncontrolled an explosion occurs.In a nuclear reactor
the fuel rods are a mix of Uranium 235 and Uranium 238. The vast
majority of the Uranium is Uranium 238 (over 99%) which does not
fission. However238U with a half-life of 4.5 109years235U with a
half-life of 7 108years234U with a half-life of 2.5 105years
Nuclear fusion is simply the joining together of smaller nuclei
to create a larger nuclei. The resulting daughter nuclei is less
massive than the original mother nuclei. The mass defect is the
cause or the source of the energy released in nuclear fusion. An
example of nuclear fusion is the fusion of deuterium and tritium:In
this reaction the deuterium and tritium combine to form He-5 which
almost immediately decays to He-4 the emission of a neutron.So back
to binding energy
To the right is a graph of average binding energy per nucleon
vs. atomic number. The greater the binding energy the more stable
the nuclei. As a result everything wants to increase its average
binding energy per nucleon. Notice that Fe-56 has the highest
average binding energy, thus its the most stable isotope.
Everything to the left of Fe-56 tends to fuse (fusion) to create a
larger heavier and more stable nuclei. Everything to the right of
Fe-56 tends to break down (fission) to become more stable.This also
means that any fission of a nuclei larger than Fe-56 will release
energy, whereas isotopes smaller than Fe-56 would require energy to
fission The opposite is true for fusion. Nuclides smaller than
Fe-56 will release energy when fused and nuclide larger than Fe-56
will require energy to fuse.Radioactive DecayATOMIC, NUKE &
QUANTUM RADIOACTIVE DECAYDescribe the phenomenon of natural
radioactive decayDescribe alpha, beta and gamma radiation and their
propertiesIn the same way that a rock at a top of hill is not
stable and has too much potential energy and wants to get rid of it
by rolling down the hill, the nucleus of an atom can become
unstable, essentially this means that it has to much energy and
wants to get rid of its energy. This can be due to the number of
protons and neutrons in the nucleus. If there are too many protons
(more than 83) then the atom is not stable no matter how many
neutrons are added (there is some thought that huge stable atoms
may be able to be created, but thats another story). Neutrons hold
the protons together, but neutrons themselves are not stable, an
isolated neutron will decay in a short period of time, if the
nucleus gets large and there is a larger number of neutrons then
neutrons become more and more isolated from protons and thus can
decay. If there are not enough neutrons then the protons will repel
each other and result in an unstable nucleus. The nucleus can also
be excited, much in the same way that electrons in orbit around the
nucleus get excited.When a nucleus is unstable it gets more stable
or loses energy in many different ways. One of the ways is natural
radioactivity decay, radioactive decay is a completely random
process that is governed by the weak nuclear force. There are three
main types of decay:Alpha Decay is the process in which the nucleus
ejects an alpha particle which is a helium nucleus, 2 protons and 2
neutronsExample:
Where a U-238 atom fissions into Th-234 and a Helium nucleus.
Alpha particles with their typical kinetic energy of 5 MeV (that is
0.13% of their total energy, i.e. 110TJ/kg), have a speed of
15,000km/s. Alpha particles do not penetrate very far, they tend to
lose their energy very quickly. This makes this not very dangerous
to humans if the radioactive source is outside the body, the alpha
particles will generally be stopped by the layer of dead skin.
However if the source is inside the body, they become very
dangerous. Radon gas is a common example of a dangerous alpha
source. Alpha decay is governed by the strong nuclear force. Alpha
particles have a large ionizing energy.Beta Decay There are two
types of beta decay, positive and negative. Positive beta decay is
the process by which a neutron decay into a proton and an electron.
The neutron is made of three quarks, one up quark and two down
quarks. One of the down quarks is converted to an up quark by the
emission of a W boson thus the quark changes flavor. Beta decay is
governed by the weak nuclear force. The electron does not have
enough energy to escape the pull of the positively charged nucleus
(protons), so the electron must quantum mechanically tunnel out of
the nucleus, that is it borrows energy to jump outside the nucleus
then returns the energy and travels away from the nucleus with its
initial energy. The emission of the electron is also accompanied by
the emission of anti-electron-neutrino. Negative beta decay is
given by the following equation:
Negative beta decay is the process by which a proton decays into
a neutron and a positron and emits a electron neutrino. The mass of
the neutron is greater than the mass of the proton. Therefore
negative beta decay does not happen without an input of energy, the
binding energy is lower in the original nucleus.
Beta particles are emitted at close to the speed of light and
thus have a much great penetration ability and therefore more
hazardous to humans, they have less ionizing energy than alpha
particles.Gamma Decay Is the process by which an excited nucleus
decays to a lower energy level, much in the same way that electrons
can be excited and decay to lower orbitals and thus releasing
energy in the form of light. In the case of the nucleus decaying to
a lower energy level energy is still released in the form of an
electromagnetic wave, but in this case which large amounts of
energy, thus a gamma ray. Gamma rays are typically defined as
photons with energy greater than 10 keV. Compare this to the
maximum energy released by an electron transition in the hydrogen
atom of 13.6 eV. Because of their high energy and no charge gamma
rays can penetrate easily and can ionize, making them a significant
danger to humans.Describe the ionizing properties of radiation and
its use in the detection of radiationThe Geiger-Muller tube and the
ionization chamber are examples of such detection devices. Only a
qualitative understanding of the operation of the devices is
required.A Geiger-Muller tube, the predecessor to the Geiger
Counter. Is a tube filled with inert gas (helium, neon, etc).
Inside the tube is a cathode and an anode, that create a strong
electric field in the tube. When the ionizing radiation enters the
tube it has enough energy to strip electrons off the gas molecules
(atoms) thus creating ions, the ions are accelerated by the
electric field. As the ions are accelerated they gain enough energy
to create more ions by collision, thus an avalanche of ions is
created and a short pulse of current is generated. The current is
detected and counted.Explain why some nuclei are stable while
others are unstableEssentially there are either not enough neutrons
to glue the protons together, thus the nucleus has an unstable
balance of kinetic and potential energy, i.e. the protons are
trying to get away from each other. There can be two many neutrons,
so that neutrons are effectively isolated from protons. Neutrons
are not stable by themselves, a free neutron, a neutron outside of
a nucleus, has a half life of about 15 minutes. A third way that a
nucleus can be unstable is if it simply has too much energy, its
like the hyperactive kid in the back of the roomDetermine the
atomic and mass numbers of the products of nuclear decay in a
transformation or in a series of transformations.Nuclear
transformations or nuclear reactions are governed by three
laws:Conservation of charge the total charge of a system can
neither be increased nor decreased in a nuclear
reaction.Conservation of nucleons the total number of nucleons in
the interaction must remain unchanged.Conservation of mass-energy
the total mass-energy of the system must remain unchanged in
nuclear reaction.Examples:
State that radioactive decay is a random process and that the
average rate of decay for a sample of radioactive isotope decreases
exponentially with time.Radioactive decay is a random process and
that the average rate of decay for a sample of radioactive isotope
decreases exponentially with time.Hmm, that was hard.Define the
term half-lifeDetermine the half-life of a nuclide from a decay
curveSolve radioactive decay problemsThe half life of a radioactive
isotope is the length of time in which one-half of its unstable
nuclei will decay.So if you have one kilogram of a radioactive
substance, after one half life you will have one-half kilogram of
the substance and half a kilo of the decay products. After another
half-life you will have one quarter of the original substance and
three quarters of a kilo of the decay substances as so on. This is
weird it should bug you.Its important to know and realize that
radioactive decay is truly a random process and can only be
described by the language of probability. After one
half-lifeapproximatelyhalf of the radioactive substance will decay
it is very unlikely that it is exactly half. With large numbers
this is not a problem, but if the sample was only 3 or 4 atoms then
we would start to have problems predicting what will occur. The
extreme would be a sample of 1 atom leading to some philosophical
questions SeeSchrdinger's cat.One last term:Activity is the number
of decays per second measured in Becquerel. More specifically 1Bq =
1 nuclear decay per second (from comments below).The half-life is
the amount of time for half of the material to decay. Thus after
one half-life there would be half as many decays occurring. So the
amount of time that is required for the activity to drop in half is
equal to the half life.The AtomATOMIC, NUKE & QUANTUM THE
ATOMDescribe a model of the atom that features a small nucleus
surrounded by electrons.A guy by the name of Bohr created a model
for the atom that consisted of an small nucleus surrounded by
orbiting electrons. There was an assumption that the electrons,
literally orbited the nucleus in a similar way to how planets orbit
a star. This model, often referred to as the Bohr model, does a
very good job of describing many of the properties of the hydrogen
atom, but fails to describe more complex atoms.An electrically
charged particle that accelerates gives of electromagnetic waves,
light. If the electrons where moving in a circular path they would
be constantly accelerating and thus constantly discharging energy
in the form of light. This would cause the electron to spiral into
the nucleus and we would see constant light emission. Neither of
these happen, a new model is needed.A new model consists of orbital
rather than orbits. The electrons still surround the nucleus, but
they do not follow a path so to speak. Instead of having a path to
follow, there is a region where the electron is likely to be. The
orbital never overlaps the nucleus. Some orbitals are not
continuous, meaning there are 2 or more regions where a single
electron is likely to be, but the electron is never in the space
between the orbitals, yet the electron can be in both
regionsOutline the evidence that supports a nuclear model of the
atomA qualitative explanation of the Geiger-Marsen experiment and
its results is all that is requiredOne of the first models for the
atom was called the plum pudding model. The model was of an atom
that was a mix of positive and negative charges equally distributed
inside of the atom, i.e. the density of the atom was uniform.Two
guys Geiger and Marsen were working with Ernest Rutherford (as
graduate students?), they conducted an experiment to explore the
insides of the atom. They shot alpha particles at a thin gold foil,
to detect the alpha particles after they pasted through the gold
file they used a screen of zinc sulfide which briefly glows when
struck by the fast moving and charged alpha particles.
The expectation was that the particles would pass through the
pudding of the atom and be deflected little if any. What they found
was that the vast majority pasted straight through the nucleus, a
few where deflected a little, but to their surprise they found that
some were deflected at large angles and some were even reflected
backwards!At the time they did not know that alpha particles were
Helium nuclei, but they knew they had a positive electric charge
and had mass. Thus the only conclusion that could be made from the
experiment was that the atom had a very small positively charge
center, now called the nucleus. The majority of the alpha particles
were not deflected because the inside of the atom is almost
entirely empty space, the few that were deflected slightly had
their trajectory altered by the repulsive electric force between
the alpha particle and the positively charged nucleus and the few
that got reflected backwards hit the nucleus like a ball bouncing
off the floor. They set out to prove the plum pudding model and
discovered the nucleus not bad for a couple of graduate
students.Outline evidence for the existence of atomic energy
levelsStudents should be familiar with emission and absorption
spectra, but the details of atomic models are not required.The Bohr
model of the atom has electrons orbiting the nucleus at distinct
energy levels, i.e. only certain orbits/energies are allowed. If a
glass tube is evacuated and the air is replaced with the gas of a
single element (molecules work too) and then an electric current is
passed through the gas then the gas will start to glow. It was
found that the color of the light given off by an element is
distinctive of that element. If the light given off is spilt into
its individual colors or wavelengths (or frequencies) it was found
that the light is not continuous but there are just a few colors
given off. Below are the spectra given off by hydrogen, helium and
oxygen, these spectra are known as emission spectra.
When light white passes through a gas, the gas absorbs some of
the light. The light that is observed is exactly the same
wavelengths that the gas emits when it is excited The spectra of
light that is not absorbed by a gas is called the absorption
spectra. Emission and absorption spectra are exactly opposite.When
the gas is excited the energy added to the atom(s) excites an
electron to a higher or more energetic orbit, after a short period
of time the electron de-excites and falls back to its original
orbit. In the process the electron losses energy in the form of a
photon (light), the energy of the photon is equal to the energy
difference between the two orbits. When white light is incident on
a gas only the photons with exactly the right amount of energy to
excite the electrons are absorbed, when the electron de-excites the
energy is released in a photon but in a random direction, thus
causing a dark line in the spectra. The uniformity of the emission
and absorption spectra are evidence for atomic energy
levels.Describe the existence of isotopes as evidence for
neutronsExplain the terms nuclide, isotope and nucleonDefine mass
number and atomic numberNot all atoms of a given element have the
same mass, yet they have all the same chemical properties. Atoms of
the same element but that do not have the same mass are called
isotopes. This suggested that there is some electrically neutral
particle that has mass inside the atom. The existence of isotopes
is evidence for neutrons.The term nuclide refers to a specific
isotope. The term nucleon refers to particles in the nucleus, i.e.
protons and neutrons. The mass number of an atom is the sum of the
nucleons in an atom. The atomic number is the number of
protons.Thus the atomic number defines what element an atom is and
if two atoms have the same atomic number but different mass numbers
then they are isotopes gee that was tough.Describe the interactions
in the nucleus.The width of the an atom is approximately one
ten-billionths of a meter or:One tenth of a nanometer is one
angstrom. While the width of the nucleus is approximately ten
thousand times smaller or about . Which means that the positively
charged protons are very close together and because of their like
charge the protons are repelled from one another with enormous
force. So how is the nucleus stable, how does it stay together?
Thats the role of the neutrons, at VERY small distances, less than
the strong nuclear force attracts the protons to the neutrons so
forcefully as to overcome the electric force As the number of
protons is increased in the nucleus the number of neutrons must
also increase, for small atoms the number of neutrons to protons is
roughly equal. However as the atoms get larger the number of
neutrons becomes larger and larger in.
Particle PhysicsATOMIC, NUKE & QUANTUM PARTICLE PHYSICS
12.3.1 Outline the concept of antiparticles and give
examples12.3.2 Outline the concepts of particle production and
annihilation and apply the conservation laws to these
processes.Every known particle has an associated anti-particle.
That is a particle that has all the opposite quantum numbers,
electric charge, lepton or baryon number, strangeness etc. As far
as we know anti-matter does not have negative mass and still falls
down. Tests have been done to see if anti-matter falls up. No
conclusion test has been done to show that anti-matter falls
up.
When a particle and its associated antiparticle collide they
completely and totally annihilate turning into pure energy, in
accordance to Einsteins relation of E = mc2. An example of this is
the annihilation of an electron and a positron (positively charged
electron, basically). When they collide their mass is turned into
energy in the form of two high energy gamma rays. During the
annihilation mass-energy and momentum are conserved.If a photon has
a higher energy than the rest mass of the electron and positron, it
is possible for a electron and positron to be spontaneously
created.12.3.4 List the three classes of fundamental particle12.3.5
State that there are three classes of observed particleThere are
over 240 subatomic particles. We classify them by how they interact
with forces. There are 3 classes of observed particles.Class of
ParticleDescriptionExample
LeptonFundamental particles. Not effected by the strong force.
There are 3 particles and associated neutrinos. Leptons are not
affected by the strong force. Leptons appear to have no geometrical
size, but they do have mass.Electron, Muon, Tau, Electron Neutrino,
Muon Neutrino, and Tau Neutrino
HadronParticles affected by the strong force. They are made up
of quarks. Include Baryons and Mesons.Protons, Neutrons and
Pions.
Exchange BosonFundamental particles that are exchanged between
other particles. The exchange is the force.Gluon, W & Z,
Photon, Graviton
Leptonscome in three families each with an associated
neutrino:LeptonMassAssociated Neutrino
Electron0.000511 GeVElectron Neutrino
Muon0.1066 GeVMuon Neutrino
Tau1.777 GeVTau Neutrino
Electrons, muons and tau particles all have the same electric
charge, but different masses. Both the muon and tau particle are
unstable and decay relatively fast. The mean life of a Muon is 10-6
seconds whereas the taus mean lifetime is only 10-12 seconds.
Neutrinos are electrically neutral, as their name suggests, where
or not neutrinos have mass is a topic of current research.
Neutrinos are so plentiful and neutral that they can pass straight
through the earth and you have millions going through your body as
you read this.In quantum physics there are many new properties that
appear to be conserved. These new conservation laws were discovered
experimentally and appear to hold true. One of the new conservation
laws is the conservation of Lepton number. Neutron undergoes
negative beta decay, it gives off an electron with a lepton number
of 1 and anti-electron neutrino with a lepton number -1. Thus the
lepton number is conserved.Hadronsare spilt into two groups,
Baryons and Mesons. Hadrons by definition are particles that are
affected by the strong force. They are some times referred to as
strongly interacting particles.Baryonsare hadrons that are made of
three quarks. Neutrons and protons are two common examples of
baryons. All baryons have spin . Protons are the only baryons that
are stable. Neutrons by themselves will break down, by beta
negative decay, into protons. A neutron has a half life on the
order of a 608 seconds and is relatively stable. There are baryons
that are many times the mass of protons or neutrons but they all
have very short half-lives and thus are not observed in daily life.
Baryons that are heavier than nucleons are call hyperons.Mesonsare
hadrons that are made of two quarks, one normal quark and an
anti-matter quark. Mesons consist of pions, kaons, eta and several
other particles. Mesons are responsible for mediating the strong
force between hadrons or nucleons.Quarks- Fundamental particles
that make up all Hadrons. Quarks can come in three different colors
and the respective anti-color, red, blue and green. The color
charge is analogous to electric or mass charge. Color has nothing
to do with the color as see by a human eye, physicists simply ran
out of descriptive terms Only white combinations are possible. In
other words neutrons and protons have a red blue and green quark.
Whereas mesons must have a quark of one color and a quark of the
anti-color Quarks are subject to the strong force via gluons, that
literally glue the particle together.In a Hadron the quarks are
held together with gluons, however the gluons can not leave the
Hadron, and thus the attraction between nucleons can not be due to
gluons, but are in fact due to gluon exchanging quark pairs, or
mesons.QuarkChargeMass
Up+2/3360 MeV
Down-1/3360 MeV
Charm+2/31500 MeV
Strange-1/3540 MeV
Top+2/3174 GeV
Bottom-1/35 GeV
12.3.6 Outline the structure of nucleons in terms of quarksSince
nucleons are baryons they are made of three quarks. The table below
shows the combination of quarks that makes up protons and neutrons.
They differ by only one quark. All matter in the world around you
is made of up and down quarks in combination with leptons. When a
proton or neutron undergoes beta decay one of the quark changes
flavor. The weak nuclear force is the only force that can change
the flavor of a quark.NucleonQuark Configuration
Protonuud
Neutronudd
12.3.3 List and outline the four fundamental interactions12.3.7
Outline the concept of an interaction as mediated by exchange of
particlesForceExchange Particle
GravityGraviton
Weak ForceW+, W- & Z
ElectromagneticPhoton
StrongGluon, pions, mesons
ColorGluon
The strong force can be seen as an extension of the color force
beyond the confines of the quarks or nucleon. In order of relative
strength, weakest to strongest:Gravity < Weak Force <
Electromagnetic < StrongIn recent years the weak force and
electromagnetic force were shown to be the same fundamental force,
which has been called the electroweak force. Work is under way to
theoretically or mathematically combine all four forces into one
force, so that all phenomena can be explained by one force!Quantum
MechanicsATOMIC, NUKE & QUANTUM QUANTUM MECHANICSDescribe the
photoelectric effect and Einsteins explanation of this
effect.Outline an experiment to test the Einstein modelWhen light
strikes a metal some of the electrons in the metal can be knocked
off an atom and can fly away or dissociate from the atom. If enough
light strikes the metal a substantial current can flow. This is the
basis for what is called the photoelectric effect.When the
experiment is done a few surprising results are found:1. The
electrons are released immediately.2. Increasing the intensity (the
amount) of light hitting the metal increased the current or number
of electrons released but did not affect the (maximum) kinetic
energy of the electrons.3. If the frequency of the incident light
is lowered, at a certain frequency the current stops flowing no
matter how intense the light.These results are incompatible with
the wave model of light. This discrepancies were well know and
people were working on it, but Einstein was the first to fully
explain the what was going on, and he won the Nobel Prize for
it.First a little background:There is a phenomena called blackbody
radiation. Any body will radiate light, the frequency of the light
is distributed over a range of frequencies. The distribution shifts
as the temperature of the body changes. The classical theory
provided an acceptable explanation at lower frequencies, however at
higher frequencies classical theory predicted that the body would
radiate an infinite amount of energy clearly impossible. A new
theory was needed.A guy by the name of Max Planck provided the new
theory. The key to Plancks theory was that the energy of light was
quantized, that is it could only take on certain energy levels. He
hypothesized that the energy of the light was given by the
equation:(1)E=hfWere h is now known as Plancks constant and f is
the frequency of the light, this equation is in the IB formula
booklet. Plancks theory provided a theoretical framework that
explained the experimental observations and quantum mechanics was
startedBack to the photoelectric effect:
Einstein used Plancks theory that the energy of light was
quantized to explain the photoelectric effect. An experiment
similar to that shown to the right can be done to test the
properties of the photoelectric effect.If the frequency of the
light is low and slowly increased it will be found that at some
frequency a current will start to flow, this is called the
threshold frequency. If the frequency of the light is well above
the threshold frequency, a negative potential can be applied in the
cathode tube, as the potential is increased the current decreases
until the current stops, the voltage that the current stops flowing
at is called the cut-off voltage (or the stopping voltage).
Therefore we can say the maximum energy of any of the electrons is
equal to:(2)E=eVsThis provides a method to measure the maximum
energy of the electrons that are given off by the metal for a given
frequency of light. If the frequency of light is increased the
current will start to flow again, thus by increases the frequency
of light we have increased the maximum kinetic energy of the
electrons. If we plot the maximum kinetic energy versus light
frequency we find the following.
The x-intercept is the cut-off frequency, or minimum frequency
of the light required to release electrons from the metal. The
slope of the line is equal to h, Plancks constant. The y-intercept,
represents the amount of energy needed to remove the electron from
the atoms, or the ionization energy.is called the work function,
how much work has to be done to release the ionize the atom. The
work function is different for different metals. From the graph we
can write a function for the energy of the incident
light:(3)E=EKmax+We also can describe the energy of the photon in
terms of Plancks constant and the frequency.(4)hf=EKmax+This
equation is in the IB formula booklet. If the incident light
frequency is the cut-off frequency then the electron will have no
kinetic energy:(5)Elight=hf0=This is the minimum energy the light
needs to have in order to generate a current. The idea of a minimum
energy does not match up with a wave model of lightWe can relate
the energy of the incident light to the cut-off frequency and the
maximum kinetic energy of the electrons:(6)hf=hf0+eVsYet another
equation in the IB formula booklet!With a wave model of light,
light is continuous and should be able to continuously give energy
to the metal, and thus an electron would be released when enough
energy was given to the metal. Einstein proposed the theory that
light is not a wave, but is a particle with quantized energy, or at
the very least that light had both wave and particle like
properties. The particles are called photons, if the incident
photon has enough energy to knock an electron off, then it is
absorbed and an electron is released. If the energy of the photon
is too low then the photon is reflected or transmittedDescribe de
Broglies hypothesis and the concept of matter waves.After Einstein
showed that light had particle like properties, a guy by the name
of de Broglie began to wonder if matter, things normally thought of
as particles, had wave like propertiesThe energy of a particle is
given by the equation:(7)E=p2c2+m20c4If the object has zero rest
mass then the energy of the object is:(8)E=pcTherefore for
light:(9)E=hf=pcSolving for momentum:(10)p=hfcThe speed of light is
defined as:(11)c=FTherefore the momentum can be described
as:(12)p=hfDe Broglie hypothesized that other particles with
momentum may have a wavelength as well. The so-called de Broglie
wavelength is:(13)=hpDe Broglie did not have substantial
experimental data to justify this conclusion it was a
hypothesis.Outline an experiment to test the de Broglie
hypothesis.A few years after de Broglie made his hypothesis three
physicist (Davisson, Germer, Thomson) independently performed
experiments that supported de Broglies hypothesis.A beam of low
energy electrons was aimed at different angles at a nickel crystal.
The electrons appeared to reflect (bounce) off the nickel. However
they found that at certain angles the electrons did not appear to
bounce off. What they realized was the pattern was the same as for
light passing through a diffraction grating. It appeared that the
electrons were interfering with themselves of each otherIf low
energy (low momentum) electrons are shot one at a time at a double
slit an interference pattern can be detected. But for an
interference pattern to form the electrons must behave as a wave.
Also if the electrons are shot one at a time, then they must pass
through both slits and interfere with themselves!To make the
situation stranger yetIt seems impossible for an electron to pass
through two slits at the same time, surely it must go through one
or the other. If a detector is set up at one of the slits, to see
if it goes through that slit, the interference pattern is destroyed
Simply by testing or measuring which slit it goes through forces
the electron to go through only one slit! This can be at least
somewhat explained by the Heisenberg uncertainty principle.Outline
how atomic spectra can be observedExplain how atomic spectra
provide evidence for the quantization of energy in atomsUmm, well,
gee, I guess you could use a spectroscopeEssentially light needs to
reflect off of a diffraction grating, this splits the light into
individual wavelength or frequencies (this is because light of
different wavelength refracts at slightly different angles). These
can then be viewed and analyzed.Atomic spectra are not continuous,
they are discrete. That is the light given off is only particular
wavelengths and is characteristic of the atom giving off the light.
The frequency of the light is discrete or quantized and the energy
of the light is dependent on the frequency, this provides further
evidence for the quantization of energy.Examples of atomic spectra
(visible light only):
Each element has its own characteristic spectra. Notice that the
number of lines increases with the size or complexity of the atom.
Each line (color) is caused be the transition of an electron from
an excited state to a less excited state. The more electrons the
atom has the more possible combinations and therefore more lines in
the spectra.Outline the Bohr model of the hydrogen atom
Niels Bohr in 1913 developed a model of the hydrogen atom that
was able to explain the emission and absorption spectra of
hydrogen. His model assumed that there were special orbits that an
electron could be in and would not radiate. In his model the
electrons literally orbited the nucleus in the same way that a
planet orbits a star. The orbits were quantized in terms of their
allowable angular momentum (rotational momentum). Therefore the
radii and the energy of the orbits is also quantized. The allowable
energy for the orbits is:(14)E1n2Where n is the orbit number, being
the lowest and most stable orbit. The energy of the orbit is the
energy required to ionize (or remove) the electron, an electron in
orbit is defined to have negative potential energy (exactly like
negative gravitational potential energy). When the electrons are
excited they jump to a higher energy orbit, eventually (actually
very quickly) the electrons drop back down to a more stable orbit
and release energy in the form of light (E&M radiation). The
energy of the light released is equal to the difference in energy
of the two orbits.For example:If an electron drops from an n = 2
orbit to an n = 1 orbit the energy released is the difference in
the energy:(15)E=E2E1In the case of hydrogen the energy in the
orbits is equal to:(16)E=kn2,k=13.6eVTherefore the energy released
in the transition is:(17)E=13.6ev2213.6eV12=10.2eVConverting to
Joules:(18)10.2eV(1.61019J1eV)=1.6321018JThe frequency of light is
given by:(19)f=Eh=1.6321018J6.641034Js1=2.461015HzWhich is gives a
wavelength of approximately:(20)=cf=1.22nmWhich is an infrared
wavelength.The reverse also happens when light is incident on an
atom and has the correct frequency (energy) the light is absorbed
and the electron is excited into a higher orbital.Not an
experiment, but some awesomeness about quantum mechanics.The reason
this happens is, as said, that light is quantized! Note how even
with the weird blinking the data fits with well known "classical
physics" laws. Got to love this stuff.State the limitations of the
Bohr modelIn the Bohr model the electron is assumed to be orbiting
the nucleus like a planet which means that it is continuously
accelerating. Any accelerating electric charge will emit E&M
radiation. In the Bohr model the orbits are special and it is
assumed that the electrons do not radiate while in the special
orbits. There is no physical reason or justification, it simply
makes the model work. The model only works for hydrogen, it can not
explain more complicated atoms. There is no justification or
explanation of the quantization of angular momentum By constricting
the electron to a known orbit, Bohrs model is also in violation of
Heisenbergs uncertainty principle.It explains a lot, but it is not
a complete model, a new model is needed.Outline the Schrdinger
model of the hydrogen atomA new proposed model for the hydrogen
atom was created by Erwin Schrdinger. His model used de Broglies
hypothesis that particles have wave properties. He proposed that
the electron formed a standing wave around the nucleus. Each orbit
corresponded to an integer number of wavelengths, i.e. the n=1
orbit is one wavelength in circumference, the n=2 orbit is two
wavelengths in circumference, etc.Schrdingers model used his wave
equation, which is used to describes the properties of the
particle. The square of the amplitude of the wave equation
represents the probability of finding the particle in a given
location. Schrdingers model no longer had the electrons in a given
location but can only describe the probability of the electron
being found in a given location! The fact that the location of the
electron is not known is in agreement with the uncertainty
principle.For the hydrogen atom Schrdingers model predicts a high
likelihood that the electron will be in a spherical orbit, which
matches up with Bohrs model. However Schrdinger is able to explain
more complex atoms and has better justification for the
model.Outline the experiment set up for the production of
X-raysDraw and annotate a typical X-ray spectrumExplain the origins
of the features of a typical X-ray spectrum
X-rays can be produced by shooting electrons at a metallic
target. As the electrons collide with the target the (de)
accelerate, thus they emit light. The frequency of the light is
dependent on the kinetic energy of the electrons. A high electric
potential is used to accelerate the electrons, thus the frequency
of the light is dependent on the potential difference.In the
diagram shown to the right a filament is heated until the electrons
are emitted, the electrons are then accelerated through a electric
potential until they strike a tungsten target.A typical X-ray
spectrum is shown to the below. There are two notable features.
First there is a continuous spectrum, this is produced by the
acceleration of the electrons. The range of wavelengths/frequencies
is only a function of the electric potential.The spikes are due to
emissions from the target. Occansionally the electrons strike the
target with the correct amount of energy to excite an orbiting
electron, when the electrons falls back down X-rays are emitted in
the characteristic peaks (frequencies).