JJ Thomson suggested the “plum pudding” model of the atom.

In 1911, Geiger and Marsden fired a beam of positive alpha particles at thin gold foil. Most passed through undeflected, showing large empty spaces in foil. BUT some deflected back at large angles, showing repulsion (rather then just collisions) – this formed the Rutherford model of the atom (central positive charge with electrons in orbit)

Problems with Model

• If electrons don’t orbit, they would be attracted to centre and atom would collapse.
• If they do orbit, then their acceleration (connected with UCM) should radiate energy. (Maxwell’s theory) and as they radiate, they will spiral in and it will collapse. When it collapses, the frequency should increase – resulting in the emission of a continuous spectrum of radiation.

If a sample of gas is energized with high temperatures or electric discharge, then a line emission spectrum is formed.(formed when the gas emits frequencies of light)

 Max Plank worked on the spectrum of radiation emitted by an object that glows when heated – black body radiation law. He stated that the walls of the solid can be seen as a series of resonators that oscillated at different frequencies. The resonators gain energy by heat from the walls and lose it from radiation. The energy at any time is proportional to the frequency. The energy could only take up a limited number of values, hence spectrum of energies was no longer continuous, therefore the energy is said to be quantized.

 Einstein extended Plank’s work to light. He suggested it acted like a stream of small bundles of energy, or quantized. His model was based on two assumptions: Light was composed of photons and the energy of a photon; E = hf.

In 1912, Bohr used Rydberg’s equation for the Balmer series (m = 2) and derived it from his hydrogen model.  He used a blend of classical and quantum physics to make three assumptions:

• All electrons orbit in fixed energy levels so they don’t radiate energy. Energy of the electron is quantized.
• Angular momentum of an electron at this level is also quantized; hence: n = principle quantum number.
• Electrons can move between energy levels by absorbing or emitting an amount of energy equal to the difference of energy between the levels. It can actually also become free from the atom, leaving it ionized.

This shows that the frequency of the photons resulting from the excited electrons dropping to lower energy states is the source of the emission lines in the spectrum of hydrogen.

Limitations of Bohr Model

• Was a blend of both classical and quantum physics.
• Only worked for Hydrogen atom.
• Zeeman splitting – when gas is excited in a strong magnetic field, the spectral lines are split into many close lines, which shows the energy of the electron has been modified in this field.
• Zeeman splitting also still occurred with the absence of the field. This is related to the electron spin.
• Further splitting is a result of hyperfine structure.
• The thought that an electron has a definite orbital radius and momentum violates the uncertainty principle.

De Brogile in 1924 proposed that not only did waves have particle characteristics, but particles had wave characteristics. Hence, every moving body should have an associated matter wave, with wavelength of:  derived from E=mc^2=hf.

Just as light behaves as both particle and waves, so does material objects. Bohr proposed the principle of complementarily that states that either the wave or photon theory, not both, is required to understand any experiment. This means the two aspects compliment each other, wave-particle duality; which applies to all matter.

Interference is when more then one wave travels through the same medium. This causes superposition to occur, with either constructive or destructive interference. To make them constructive, the waves must be coherent, or in-phase.

 Diffraction is the bending or spreading when light passes through small openings, around obstacles or sharp edges.

In 1927, Davisson and Germer proved De Brogile’s proposal by an experiment involving scattering of a low energy electron beam from a single nickel crystal. This is the first application of particle waves. They built a vacuum apparatus to measure the energies of electrons scattered from a metal surface. Electrons from the heated filament were accelerated by voltage and allowed to strike the surface of nickel. The electron beam was directed at the nickel, which would be rotated to observe angular dependence of the scattered electrons.

At certain angles there was a peak in the intensity of the scattered electron beam. This indicated wave behaviour for the electrons, due to the regular spacing between atomic planes in the crystal acted as a diffraction grating for electron waves. It can be determined by Bragg’s law to give values for the lattice spacing in the nickel crystal.

De Broglie’s ideas eventually led to a wave mechanical model of the atom, by Erwin Schrödinger.

Werner Helsenberg developed matrix mechanics, which was a mathematically equivalent model to the wave mechanics. In 1927 he developed the uncertainty principle – this states that it is impossible to make simultaneous measurements of a particle’s position, velocity and energy with unlimited accuracy. Hence, for an electron orbiting, the position, velocity and energy are not known. This principle helps explain the way in which either the wave nature or the particle nature of an electron may become more or less fuzzy in a given situation.

The Pauli Exclusion Principle states that no two electrons in the same atom can ever be in the same quantum state. If this system wasn’t correct then electrons would radiate energy away and end up in the lowest energy state, rather then filling the other shells and creating the electronic configurations.

 Atomic Nucleus: In 1932 Chadwick used nuclear reactions to prove there was such thing as a neutron. This was difficult because it didn’t interact with electric or magnetic fields. Although it could be proven by nuclear reactions and the use of Conservation of Mass and Energy.

If a neutron shot through Beryllium and then struck a proton rich material (paraffin) then a proton may be ejected. When this happened, the mass of the neutron could be calculated by conservation laws.

The nucleons (major nuclear particles) were shown to be protons and neutrons. This developed the proton-neutron model of the nucleus by Heisenberg where the atomic number and number of protons is Z, while number of neutrons is A-Z, with A being the atomic mass number.

Nuclear transmutations (changes in nucleus’ structure): Radioactivity refers to particles and energy being emitted from the nuclei by nuclear instability. The nucleus experiences both electromagnetism and the strong nuclear force; hence, there are many nuclear isotopes who are unstable and emit radiation. (alpha, beta and gamma) Alpha is most ionizing which is formed by a doubly charged helium nuclei. Beta consists of high speed electrons. Gamma is high energy, short wavelength electromagnetic radiation.

 By emitting radiation, the nucleus may be transmuted into another element. The new element may be radioactive, and then also decay into another element and so on in a “radioactive series until it is stable. Some gamma rays can be emitted in decay as the nucleus gives off energy to become stable.

 A given element always decays at the same rate, independent of heat and pressure. It can not be predicted when a particular nucleus will decay.

The rate of decay of a radioactive element is given by its half life, which forms an exponential curve.

Detection of radiation: Different radiation has different properties including: ionization power, penetration ability and behaviour in both electric and magnetic fields. (Gamma rays have no charge, therefore no deflection. Alpha and Beta go opposite directions due to their opposite charge)

The radiation in which is more ionizing will be more likely to interact with matter and the penetration is inverse proportion to the ionizing ability. Hence, alpha particles can be stopped by a sheet of paper, beta by aluminum and gamma by a slab of concrete)

 Ion chambers detect radiation by electron-ion pairs formed by passage of radiation through gas, creating an electric signal. The more pair produced, the bigger the current pulse. Example is the Geiger counter.

Track detectors view the tracks of a charged particle in a known magnetic field; this can solve the energy and momentum of the particle. Example is a photographic emulsion where the charged particle ionizes the atoms in the emulsion layer.

Cloud chamber: this is when a gas is super-cooled and is subject to ionizing radiation. The ions form centers for condensation so that the particles produce tracks.

Bubble chamber: this uses liquid that is maintained near the boiling point. The ions produce a bubble track as the liquid boils around the ions.

Nuclear structure: The nucleus is formed from protons and neutrons, hence Yukawa suggested a force which was always interchanging between nucleons of a particle called the meson or the pion which would hold the nucleus together against the force of repulsion between the protons. This is known as the nuclear force and is short ranged. This force is very powerful and attractive between all the nucleons. There are also short range forces which each nucleon affects 3 or 4 of its neighbors. The electrostatic force is a long-range force which has some influence on all protons in the nucleus. Stability depends on both of these forces.

Nuclei can be unstable due to a large mass. This is because the longer range forces of electrostatic repulsion become dominant then the short range. If there is not much mass, stability also decreases because the nucleons cannot be considered to be surrounded by others, hence, the nuclear force isn’t strong and the electrostatic force dominates.

Instability can also occur when the ratio of neutrons to protons is not correct. This is a balance between the electrostatic repulsion and the nuclear attraction and increases with size of the nucleus  (longer range electrostatic forces)

To become stable, atoms may undergo radioactive decay. This may include:

• Surplus of neutrons (neutrons reduced): The neutron turns into a proton, an electron (which is ejected) and a neutrino (no mass; but obeys conservation of energy laws). Gamma radiation is sometimes ejected to emit the “excess” energy.
• Surplus of protons: when a proton is converted into a neutron, a positron (positive electron) and an antineutrino.
• Surplus of neutrons and protons: Mass may be lost by emission of alpha particles. The energy of this particle is lower then expected, which shows that the alpha escapes by quantum mechanical tunneling.

Neutrino: Proposed by Pauli to account for the loss of energy of beta emission. He suggested this energy was carried away by the neutrino in the form of angular momentum. This was shown in 1956. It was hard to show their existence because they only interact slightly with matter so that they can pass through Earth without being absorbed, and having no charge meant they didn’t interact electromagnetically.

 Nuclear binding energy and mass defect: Nuclei is made up of protons and neutrons, but the mass of the nucleus is less then the sum of the individual masses of the neutrons added up. The difference is known as the mass defect and is a measure of the nuclear binding energy which holds the nucleus together. To break up an atom, energy is required, and to fuse particles together results in the release of energy (in radiation). This energy is not needed since the nucleons bind into a stable nucleus, rather then being separate. The binding energy can be calculated by Einstein’s relationship: E=mc^2.

Binding energies of nucleons are in the range of millions of electron volts. The atomic transition might emit a photon in the range of a few electron volts, in the visible light range; the nuclear transitions can emit gamma-rays with energies in the Mega-electron volt range.

 The binding energy curve is obtained by dividing the total nuclear binding energy by the number of nucleons. It has a peak which shows that there is a region of stability where there is either a breakup of heavy nuclei or a combining of lighter nuclei.

Nuclear fission: in the early 1930’s Fermi bombarded uranium with slow neutrons which created new radionuclides. Hahn and Strassman, while attempting to identify the expected elements, found several unidentified lighter products. Meitner realised that Hahn’s lighter products from the neutron bombarding were coming from the fission of U-235.  Frisch and Meitner showed that U-235 fission yield an enormous amount of energy, and the fission lost at least two neutrons for every neutron absorbed in the interaction. This made a chain reaction with an unprecedented energy yield. As part of the Manhattan project, Fermi built an atomic pile which held the world’s first self-sustaining nuclear chain reaction in 1942. The structure was formed by uranium in combination with graphite blocks to slow the neutrons to thermal velocities to enhance neutron capture. Cadmium rods inserted in the “pile” were used to control the reaction rate.

If at least one neutron from each fission strikes another U-235 that initiates fission, then the chain reaction is sustained. With less then one neutron striking another, then the event will fade off. If more the one then it will be an uncontrolled chain leading to massive energy release in a short time.

Nuclear reactions obey the laws of conservation of mass and energy. Spontaneous nuclear reactions are possible when there is a release of energy as the reactants form the product. The energy released in each fission can be calculated by the conservation of mass and energy. The amount of energy which is released can be calculated by looking at the difference between the mass of the reactants and the products. The mass difference calculated energy by E = mc^2.

Nuclear fission reactor: Fancy way of producing steam to produce electricity. It consists of: Containment structure (radiation shield), fuel source (fuel rods of uranium), control rods (which regulate rate of reaction), moderator (to slow neutrons down and capture more) and coolant (transfers heat)

Fuel rods: made of enriched uranium to increase probability of fission occurring. If at least one neutron from the uranium strikes another nucleus it causes fission as well as a chain reaction. If the reaction will sustain itself then it is said to be critical.

The neutrons in fission reactions have high energies; therefore they must be slowed down to operate in the reactor, by moderation. When neutrons collide elastically with other nucleus’ which are at rest, it transfers energy to it. Water and carbon are commonly used as moderators, as its heavy water.

Since a chain reaction relies on at least one neutron from each fission being absorbed by another nucleus, the reactions can be controlled by control rods. These are made of material in which absorbs neutrons. In a nuclear reactor, fuel assemblies are put in place and the control rods are slowly lifted until a chain reaction can be sustained. As the reaction proceeds, the number of uranium nuclei decrease and the fission-by-products which absorb neutrons build up. To keep the chain reaction, the control rods must be withdrawn abit further. At some point, the chain reaction cannot be maintained and the fuel must be replenished.

Neutron probes: Neutrons have a wavelength that is similar to the spacing between the atoms in molecules. This means they can produce interference patterns from the atomic lattice and can be used liked the electron scattering to deduce the internal structure of materials. Since they are also electronically neutral they have advantage as they can pass through the atomic electron cloud to the nucleus. They are more penetrative then electrons and x-rays. They also give unique information about elements like Hydrogen.

 Neutrons have a magnetic moment to reveal magnetic structure. Since they have energy similar to the vibrational energy of atoms in solids and liquids, they can see the motions of the atoms in molecules in great detail. The mass of the neutron may also be used when the neutron is being used as a probe, with conservation of momentum allowing information about target materials to be deduced.

The Manhattan Project: This was about American program to construct the first two atomic bombs during WW2. The world knew little about this project until the first one exploded over Hiroshima on 6th August 1945. The theory that an explosion could be brought by atomic fission was discovered in 1939. They discovered that when uranium atoms can fission when struck by neutrons to split other atoms in a chain reaction, releasing large amounts of energy. Two Hungarian physicists who had migrated to the US, Szilard and Wigner, alerted the US government of possibilities of an atomic bomb. Along with Einstein they wrote a letter to the President warning that Nazi Germany might be working on a uranium bomb. The president set up an advisory committee on uranium in October 1939. American scientists discovered that the uranium that fissions is an isotope, uranium-235, and questioned whether significant quantities could be separated (as this isotope was only 0.7 per cent of uranium). Much work was done at Columbia University in NY, and the military office was located in Manhattan, hence the name, Manhattan Project.
Meanwhile, in Britain, two immigrant physicists, Frish and Peierls, stated that an atomic bomb made of uranium-235 was possible. The told the British authorities in 1940 by showing how a bomb is produced. After more studies, they set up a project to also build an atomic bomb.

US and Britain exchanged information on weapons developments. British progress convinced the Americans in 1941 that this bomb could be created. In November of 1941 a committee of scientists was created to research. The Japanese attack on Pearl Harbor has brought the US to war. Americans were still worried that Germany were making their own atomic bomb. In the University of Chicago, scientists were working with Fermi to create the world’s first atomic chain reaction in an atomic creator in December 1942. The program was going to build two kinds of atomic bombs: one using uranium-235 and another using plutonium. Due to the time restrictions, both the teams concentrated on a way to split uranium. One method was gaseous diffusion: the uranium is turned into a gas and then passed through many membranes again and again so that the lighter uranium-235 gets through and the rest gets left behind. The other method is by electromagnetic separation, atom by atom developed by Lawrence. Both methods were expensive and involved difficult engineering. The gaseous diffusion plant did most of the separation; this was a huge plant that was around 1km long and covering 17.8 hectares. The uranium coming from the plant was given to the electromagnetic separation plant to refine it still and making pure uranium-235. These plants required large amounts of electricity, which forced the small town of Oak Ridge to have their own power plant.

In 1943 another town at Los Alamos was created in New Mexico for the Manhattan Project; this is where the bombs were designed and assembled. The physicist Oppenheimer chose it for its remoteness and many great physicists were brought to work with him such as: Szilard, Wigner, Bohr, Bethe, Teller and Feynman. Along with Oppenheimer’s great achievements was to maintain the free exchange of scientific ideas at Los Alamos, where they worked in secrecy.

How the bombs worked:
A chain reaction starts in fissionable material once enough of it has been brought to form the “critical mass”. The mechanism of an atomic bomb brings together enough fissile material to form a critical mass, and holds it together for a very short while the chain reaction takes place. The first method was the gun method. A piece of fissionable material is fired into another so that at the moment of impact, the two create the critical mass needed, this only worked for Uranium-235. For plutonium, a faster method had to be invented, something they called: implosion. The plutonium is shaped like a sphere, and high explosives are packed all around it, and detonated so that the sphere is compressed into a critical mass. A neutron initiator is incorporated into this to guarantee that a chain reaction occurs immediately. The shock waves from the explosion that compresses the material are made to arrive at the same time by distorting them through specially constructed lenses consisting of high explosive. The plutonium bomb was tested on July 16th 1945 in New Mexico. Code name Trinity, the test bomb, exploded with such power that was equivalent to 20, 000 tonnes of TNT. On August 6th, the Uranium-235 bomb was dropped over Hiroshima, and the Manhattan project was made public. The plutonium bomb was dropped on Nagasaki 3 days later. The following day the Japanese government surrendered. The first atomic bomb killed 129,588 people, the second killed 66,000 people.

Fission bomb:
The first atomic bomb used in warfare was dropped by US on August 6th 1945. Called “little boy”, it produced an explosion that killed tens of thousands of people in less then one minute. “Little boy” was a gun-type fission boy, that generates a nuclear explosion by firing one piece of fissile material into another of the same type. The bomb is gun-like in that a small wedge of uranium is fired at a larger target piece. Upon impact, the two pieces fuse together briefly, forming a supercritical mass. The rapid release of massive amounts of energy in a limited volume creates the explosion. In “Little Boy”, a mass of uranium about the size of an apple produced an explosion equal to 20 kilotons of TNT.

 The particle accelerator: The discoveries of the electromagnetic unification (b/w weak nuclear force and the electromagnetic force) was done by particle accelerators. Establishing the Grand Unification (electromagnetism, strong and weak nuclear force and gravity) cannot be done in laboratories, forcing physicists to look out to the astrophysical phenomena which may have enough energy to shed some light on further attempts at unifying the four fundamental forces. Efforts of formulating the Big Bang model were stimulated by evidence like 3K cosmic background radiation. But when modeling a very-hot, high-energy universe where matter would be very different then what it is today, they found it necessary to make use of the results of the particle physicists at the high energy accelerators.

Linear accelerators:
The particle is accelerated in a straight line, and it worked by electromagnetic waves to provide a varying electric and magnetic field wave traveling down the accelerator. These waves push the electrons are microwaves fed into accelerator structure via the wave guides.

Circular accelerators:
This gives the particle small boosts of energy each time it passes a particular point. More practical then linear, as they don’t use as much distance. They begin with the cyclotron made by Lawrence in 1929. It consists of two large dipole magnets which were designed to produce a semi-circular region of uniform magnetic field, pointing downward. These were called D’s (D-shape). The two D’s were placed back to back with their straight sides parallel but separated. An oscillating voltage was applied to produce an electric field across the gap. Particles injected into the magnetic field of the D trace out a semicircular path until they reach the gap. The electric field in the gap then accelerates the particles as they pass across it. The particles now have higher energy as they follow the path in the next D with larger radius so that they reach the gap again. The electric field frequency must be just right so that the field’s direction is reversed when they reach the gap. The field in the gap once again accelerates the particle into the other D. The particle gains energy as they spiral around. When the particle speeds up they trace a larger arc so they always take the same time to reach the gap. Hence, the constant electric field continues to accelerate them. The only thing limiting the energy is the size of the D magnets and the strength of the magnetic fields. Using superconductors will help achieve high enough magnetic fields.

A synchrotron is a circular accelerator which has an electromagnetic resonant cavity to accelerate the particles. As the particles increase in energy, the strength of the magnetic field is used to steer them much be changed with each turn to keep the particles moving in the same ring, The change in the field must be the same as the change in energy or the beam will be lost.

Current models of matter: In the 1930’s, protons, neutrons and electrons were the smallest objects into which matter could be divides and they were known as “elementary particles”. It is now known that protons and neutrons are made up of quarks. Over 100 other “elementary particles” were discovered between 1930’s and now. They are all made up of quarks and anti-quarks. These particles are known as hadrons. Leptons still appear structureless. In the modern theory, there is a “Standard model” which is made up of 12 fundamental particle types and their corresponding anti-particles. The matter particles are divided between quarks and leptons. Force carrier particles are responsible for strong, electromagnetic and weak interactions. These are also fundamental particles.

The four fundamental forces each have their own exchange particle. The standard model links the electromagnetic force and the weak force in the Electroweak Theory, and explains the strong force in terms of a quantum property known as colour, in the theory of Quantum Chromodynamics (QCD).

Particles that interact by strong interaction are called hadrons. They are also composed of quarks. This includes musons, which is a combination of quarks and anti-quarks; and baryons, which is combined of three quarks.

Quarks are thought to be the fundamental particles with charges of –1/3e and 2/3e and come in six flavors. They never occur in isolation, being confined by the colour force.

 Leptons do not interact by strong forces. They have a charge of 0 or –e and also come in six flavors.

Applications of radioactive isotopes

Medicine: Diagnostic applications: They give doctors the ability to “look” inside the body at soft tissue and organs. They are carried in the blood which allows doctors to detect clogged arteries and check functioning of the circulatory system. A radioactive tracer may be chemically attached to a compound that will concentrate naturally in an organ or tissue to get a picture taken. This is known as labeling. Since radioactive isotopes have a half-life, they are preferred in the use of drugs to minimize radiation to the patient.
Medicine: Therapeutic applications: When cells are exposed to high levels of radiation, they will be destroyed and damaged. Hence, in the treatment of cancer. The teletherapy unit destroyed malignant tumors with gamma radiation.

Industry: Irradiation and treatment of materials with radioisotopes: Radiation can destroy germs, bacteria which can contaminate blood supplies and even our food. Although with neutron radiation, the material can become radioactive itself because the neutrons are absorbed by the nucleus of the atoms in the material. Wood and plastic treated with gamma radiation are used for some flooring in high-traffic areas as they resist abrasion.

Industry: Measuring and testing applications: As radiation passes through material, it is scattered or absorbed. The amount of radiation passing through depends on the thickness and density of matter, hence radiation is used to monitor and control the thickness of materials. Radioactive tracers can be used to gauge the structural integrity of roads, buildings and bridges. They can also be used to test for the presence of certain materials.

Agriculture: Food Irradiation: Radiation can be used to destroy bacteria in food and control insect and parasite infestation. The radiation passes through the food leaving no radioactive residue, although some concerns have been raised about the chemical changed that may alter in the finished product. They can also be used to understand chemical and biological processes in plants.