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).