HHHHSC SC SC SC PhysicsPhysicsPhysicsPhysics Revision Revision Revision Revision OptionOptionOptionOption David Pham

# From Quanta to Quarks 1. discuss the structure of the

Rutherford model of the atom, the existence of the nucleus and electron orbits

Prior to the development of Rutherford’s model, the main hypothesis of atomic structure was the plum pudding model, which was based on negative charged embedded in a positive structure. This was developed by J.J. Thomson after his discovery of the electron. The Rutherford model of the atom was based upon his alpha-particle scattering experiments. This involved firing a collimated beam of alpha radiation into a thin gold foil. By the plum-pudding model, Rutherford expected most of the alpha particles to pass through mostly undeflected. However the results were different.

The observation indicated that while most of the particles passed through

undeflected, a small number bounced straight back to the source. Also, a small number of particles exhibited minor deflection. This was inconsistent with the plum pudding model and thus Rutherford proposed his ‘planetary’ model of the atom. This consisted of a nucleus, around which electrons orbited (these circular orbits are likened to the solar system). This nucleus consisted of positive charge and relatively large mass concentrated into a small volume. The electron clouds do not significantly affect the movement of alpha particles. However the presence of these orbiting electrons caused a problem for physicists. As these electrons are orbiting around a nucleus, they are accelerating, causing them to lose energy via electromagnetic radiation (underlying principle of classical physics). This would mean they’d spiral into the nucleus, creating a lack of electron clouds. Rutherford could not explain this.

discuss Planck’s contribution to the concept of quantised energy

Planck, from his studies of the black body radiation and its apparent inconsistencies with classical physics, attempted to find an elegant solution. The predictions made by classical physics and the observations of this black body radiation clashed, especially with regards to the photoelectric effect (refer to ‘From Ideas to Implementation’ notes). In order to explain these inconsistencies he introduced the concept of quantised energy, stating that energy within a black body is exchanged in small packets called quanta, which each have energy proportional to its frequency. This ushered in the notion of quantised energy, which underpins much of modern physics today. Even though Planck was uncomfortable with this idea, he is credited as the forerunner of quantum physics.

* perform a first-hand investigation to observe the visible components of the hydrogen spectrum

• See Attachments • See Prac Book

define Bohr’s postulates In atomic physics, the Bohr model created by Niels Bohr depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus – similar in structure to the solar system, but with electrostatic forces providing attraction, rather than gravity. Bohr’s model of the atom was based on his postulates. Electrons in an atom exist in ‘stationary states,’ in which they are stable and do not lose energy. They can only move to other energy states, not in between (i.e. quantised energy states). This is in opposition to classical physics (see discussion above) and explains the presence of electron orbits. No radiation is emitted by these electrons as they accelerate around in centripetal motion. The energy of an electron can only be changed if it moves into a different energy state. This energy change would be accompanied by the emission or absorption of a photon.

An electron in its stationary state has a quantised angular momentum. It is an integral multiple of ħ (h-bar is equal to Planck’s constant divided by 2π)

analyse the significance of

the hydrogen spectrum in the development of Bohr’s model of the atom

The ‘hydrogen spectra’ is the characteristic set of lines (emission/absorption spectra) which is unique to hydrogen. This hydrogen spectrum is formed when electrons move in between energy levels, but this was not known at the time of observation. However, Bohr realised that the importance of the hydrogen spectra, and incorporated it as the basis of his theory. He had realised that the oscillations of electrons in atoms produce the radiation characteristic to each element. Once he saw Balmer’s equation he realised how electrons could be arranged and how quantum ideas could be introduced. He attempted to apply Planck’s quantisation of energy concept to the atom as it seemed a natural evolution from Rutherford’s planetary model.

The model's key success lay in explaining the Balmer formula for the spectral emission lines of atomic hydrogen; while the Balmer formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. The hydrogen spectra was explained by Bohr as the movement of electrons through different energy levels. Not only did the Bohr model explain the reason for the structure of the Balmer formula, but it provided a justification for its empirical results in terms of fundamental physical constants. Note the angular momentum quantisation – this allows one to derive the empirical Balmer equation by analysing electron transfers to and from the 2nd electron shell.

describe how Bohr’s postulates led to the development of a mathematical model to account for the existence of the hydrogen spectrum:

* solve problems and

analyse information using:

Bohr’s postulates led to the derivation of an equation which could account for the hydrogen spectra. From his angular momentum quantisation condition, it could be derived that:

Also, from his 2nd postulate, electrons could only lose energy through moving from one level to another. And from Planck’s quantum theory:

Therefore, after equating the two:

We see this is equivalent to the Balmer-Rydberg equation, as

As such we can see how Bohr’s postulates lead to the development of the mathematical model to account for the existence of the hydrogen spectrum, confirming the previously empirical Balmer-Rydberg equation.

• Skill * process and present

diagrammatic information to illustrate Bohr’s explanation of the Balmer series

We note how Bohr’s model was developed with emphasis on Balmer’s empirical formula for the Balmer series of hydrogen.

Bohr’s model of the atom explained the emission spectra of single-electron atoms via the transfer of electrons between energy shells. He explained the Balmer series/equation, using the derivations from his angular momentum conservation and 2nd postulate, which stated that the only energy change came from electron movement between stationary states. From these conditions Bohr could derive an equation equivalent to Balmer equation, and he could derive the constant from physical values. The Balmer series corresponded to the electron transfers to the 2nd energy level, and was in the visible spectrum. Subsequently more series were discovered, illustrated above. These had wavelengths outside of the visible spectrum.

discuss the limitations of

the Bohr model of the hydrogen atom

* analyse secondary information to identify the difficulties with the Rutherford-Bohr model, including its inability to completely explain: • the spectra of larger

atoms • the Zeeman effect

The Bohr model of the atom had several deficiencies. It has the following limitations: • It could not predict or explain the spectra of larger, multi-valent atoms

(however it could predict the spectra of larger single-valent atoms such as the helium ion, by modifying the value of E1 appropriately). This is because it fails to account for the presence of other electrons, which modifies the mechanics of electron transition.

• It could not account for the existence of hyperfine or fine spectral lines. These are very thin lines which were observed with better instruments. There must have been some splitting of the energy levels and the Bohr model could not explain this. Later on this was found to be caused by relativistic and subtle effects, as well as electron spin.

• the existence of hyperfine spectral lines

• the relative intensity of spectral lines

• It could not explain the Zeeman effect. This is the phenomenon in which spectral lines split when the elemental gas is placed in a magnetic field. This was later explained by electron spin and orbital magnetic fields.

• It could not explain the relative intensity of spectral lines. The Bohr model could not explain why some transitions are favoured over others.

In addition, there were other shortcomings. For example, the model was a strange mix of quantum and classical physics, which are mutually incompatible. As such, it is now considered an obsolete scientific theory, as it has been superseded by more accurate models.

2. describe the impact of de Broglie’s proposal that any kind of particle has both wave and particle properties

explain the stability of the electron orbits in the Bohr atom using de Broglie’s hypothesis

* solve problems and analyse information using:

Louis de Broglie’s doctoral thesis dealt with wave-particle duality – that is, he proposed that all particles have a wave nature and all waves had a particle nature. In this he argued that nobody had managed to perform an experiment conclusively depicting light as a particle or a wave, and that the explanation of this was that particles and waves are intrinsically linked. He was able to take this idea and develop it mathematically. By noting that

and

Thus

and

As

then

Thus as

then

Therefore, the de Broglie wavelength of a particle is given by:

• Skill Initially de Broglie’s theory was deemed to have little physical significance. However, de Broglie had initiated the revolution in which other scientists would develop quantum mechanics. Quantum mechanics is a branch of modern physics dealing with the behaviour of matter and energy on the scale of atoms and subatomic particles or waves. In this theory, particles have both a wave and particle nature. The acceptance by the general physics community of quantum mechanics is due to its accurate prediction of the physical behaviour of systems, including systems where Newtonian mechanics or general relativity fails. Through a century of experimentation and applied science, quantum mechanical theory has proven to be very successful and practical in describing many phenomena. Bohr’s model of the atom, as previously explored, is inadequate in fully describing and explaining the inner workings of atoms. However, with the advent of de Broglie’s hypothesis this could be explained, as de Broglie proposed that electrons had a wave nature. He proposed that the orbits of electrons in the hydrogen atom were similar to standing waves in a ring. Standing waves are special in that they do not allow energy to propagate – that is, electrons cannot lose energy if they are in a standing wave. As de Broglie proposed that electrons set up a standing wave around its orbit, we can see that they do not lose energy, explaining Bohr’s stationary states. In order for a standing wave to be present in a ring, the circumference needs to be an integral multiple of the wavelength. Otherwise, the vibrations quickly cancel out as destructive interference occurs.

as opposed to

We shall calculate the condition necessary for the standing wave, by considering the de Broglie wavelength of the electron and the condition that there is an integral number of wavelengths in a ring.

and

So

thus

This equates to Bohr’s quantisation of angular momentum condition (his ‘3rd’ postulate). As such, we can see how de Broglie explained the unexpected stability of electrons in Bohr’s orbits with the wave nature of electrons, as they set up a standing wave in which they do not lose energy. Subsequently, with further research and development of atomic theory some of the shortcomings of the Bohr model could be explained. This allows for us to account for the stability of electrons in Bohr’s model and provide a basis for his quantisation condition. It also subsequently led to the development of quantum physics and the new quantum mechanical model of the atom today, overcoming/explaining the shortcomings of the Bohr model. Quantum theory, as discussed above, is a very powerful physical theory and widely in use today. Thus we can see the enormous impact of de Broglie’s work on wave-matter duality.

define diffraction and identify that interference occurs between waves that have been diffracted

Diffraction is the phenomenon when a wave encounters an obstacle and has its path disrupted. It is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings. It occurs when light passes through a very finely ruled grating or passes through a small opening, or passes a barrier. It is not easy to observe because the dimensions of the barrier or opening must be comparable to the wavelength of the light. In this course we are mainly concerned with diffraction gratings. These cause interference between the waves that have been diffracted, due to wavefront interactions. Each slit only allows one point on the wave to propagate, and by Huygen’s law the pattern below is observed. For example, a diffraction grating causes interference:

A series of alternating bright and dark spots can be seen due to alternating constructive (wavefronts coincide in phase) and destructive interference (wavefronts out of phase).

describe the confirmation of de Broglie’s proposal by Davisson and Germer

Davisson and Germer were able to confirm the wave-matter duality principle, by observing that electrons had a wave nature (that is, they showed interference properties once thought to be exclusive to waves).

Initially these two scientists were examining the scattering of electrons by the surface of nickel. Even though it appeared smooth, at a microscopic level this nickel was rough and caused haphazard scattering of electrons. Davisson and Germer stumbled onto the diffraction of electrons by accident. After annealing a piece of nickel, they unwittingly created large single crystal sections which could act as diffraction gratings. Now the results were much different to before. Being familiar with x-ray diffraction and de Broglie’ theory, they recognised the diffraction of electrons. As diffraction is a property of waves, not matter, this was taken as confirmation that electrons had wave properties, showing that de Broglie’s proposal of wave-matter duality was true.

* gather, process, analyse and present information and use available evidence to assess the contributions made by Heisenberg and Pauli to the development of atomic theory

Heisenberg and Pauli both contributed to our understanding of atomic theory in varying ways. Heisenberg’s most famously quoted contribution is the development of the Uncertainty Principle.

The value of the indeterminacy varies from source to source

^^ use this

This implies that quantum mechanics is non-deterministic in nature, and uncertainty is inherent. Quantum mechanics deals with probabilities rather than discrete values. Heisenberg also developed a completely mathematical model of quantum physics. He viewed the atom in terms of its observable properties, rather than as a visual model. He also applied quantum physics to the nucleus, eventually allowing other scientists to expand on this theory. Pauli’s main contribution to atomic theory is his ‘exclusion principle.’ This states that no two electrons in the same atom can have the same set of four quantum numbers. It explained the electron configuration of elements, their properties and periodicity. Electrons are built from the ground-state upwards (aufbau principle) rather than clustering in the lowest state. It is an integral part of quantum theory. In addition, Pauli also applied quantum mechanics (with difficulty) to the hydrogen atom, deriving Balmer’s equation and Rydberg’s constant, showing how the empirical equation is consistent with quantum theory. Pauli also predicted the existence of the neutrino to explain the discrepancy between the beta decay energies. This was done to ensure that the law of conservation of energy remained consistent (the particle is now known as an antineutrino). As such, the contributions of both these scientists to atomic theory allow us to expand our knowledge of how the world works on a quantum scale.

3. define the components of the nucleus (protons and neutrons) as nucleons and contrast their properties

Nucleons are the particles present in a nucleus, and they are a subset of baryons. These include protons and neutrons. They are subatomic particles, and were initially thought to be fundamental particles (but we now know they are composed of quarks). Some of the more relevant properties: Nucleon Property Proton Neutron

938 MeV 940 MeV Mass 1.673 x 10-27 kg 1.675 x 10-27 kg

+1 0 Charge +1.602 x 10-19 C 0 C

Quark Composition u,u,d u,d,d Spin +1/2 +1/2 Magnetic Moment 2.79 nuclear magnetons -1.91 nuclear magnetons

They are both bound by the strong nuclear force into atomic nuclei. discuss the importance of

conservation laws to Chadwick’s discovery of the neutron

Bothe and Becker had initially identified an unknown form of radiation. To observe this, they fired alpha particles (from polonium) at a sheet of beryllium. This unknown radiation seemed to be similar to gamma rays, as they had exceptionally high energy and penetrating power. However their energy and penetrating power was higher than previously observed gamma rays. The Joliot-Curies performed a further experiment to determine the nature of this

radiation. They allowed this unknown radiation to strike a sheet of (proton-rich) paraffin wax, causing protons to be knocked out (these protons had very high energy). This was important, because as protons have charge, their momentum and kinetic energy could be measured (an electric/magnetic field can be applied to measure these). The values of proton energy/momentum would be compared to the incident unknown radiation. As momentum and energy are conserved, the initial momentum and energy of the radiation can be calculated. It is also noteworthy that for a proton to be ejected at 5MeV then the equivalent incident gamma radiation would need 50MeV energy. However, the energy of alpha particles was noted to be 5MeV only. This would have been inconsistent with the principle of conservation of energy.

Using the principles of conservation of energy and conservation of momentum, Chadwick could calculate the momentum and kinetic energy of the incident radiation. By comparing these values, he could identify the nature of this unknown radiation. He suggested that in fact the new radiation consisted of uncharged particles, and he performed a series of experiments verifying his suggestion. He made measurements of the recoil of nuclei of hydrogen and nitrogen after interactions with his proposed neutron. The measurements were difficult (and they also involved elastic collisions – conservation of energy, and conservation of momentum) but it led to a predicted mass similar to that of a proton.

define the term ‘transmutation’

describe nuclear transmutations due to natural radioactivity

Transmutation is the process in which once element is changed to another, either artificially or naturally. Natural transmutation occurs when radioactive elements spontaneously decay over time to transform to more stable elements. Some examples of naturally occurring radiation include alpha, beta and gamma radiation.

Alpha +

Mass number decreases by 4 and atomic number decreases by 2 Beta +

No change in mass number, atomic number increases by 1 Gamma * + γ No change in mass or atomic number

Less commonly encountered are spontaneous nuclear fission, positron emission, and neutron emission. Electron capture results in the spontaneous emission of an X-ray.

* perform a first-hand investigation or gather secondary information to observe radiation emitted from a nucleus using Wilson Cloud Chamber or similar detection device

The cloud chamber is a device used to detect ionising radiation. It is a supercooled, supersaturated chamber containing water or alcohol vapour. The diagram above is of a diffusion cloud chamber, while the Wilson cloud chamber relies on expansion (not the apparatus above). • In Wilson's original chamber the air inside the sealed device was saturated

with water vapor, then a diaphragm is used to expand the air inside the chamber. This cools the air and water vapor starts to condense. When an ionizing particle passes through the chamber, water vapor condenses on the resulting ions and the trail of the particle is visible in the vapor cloud.

• The diffusion cloud chamber differs from the expansion cloud chamber in that it is continuously sensitized to radiation, and in that the bottom must be cooled to a rather low temperature, generally as cold as or colder than dry ice. Alcohol vapor is also often used due to its different phase transition temperatures. Dry-ice-cooled cloud chambers are a common demonstration and hobbyist device; the most common fluid used in them is isopropyl alcohol.

• The bubble chamber similarly reveals the tracks of subatomic particles, but as trails of bubbles in superheated liquid. Bubble chambers can be made physically larger than cloud chambers, and since they are filled with much denser material, they reveal the tracks of much more energetic particles. These factors rapidly made the bubble chamber the particle detector of choice, so that cloud chambers were effectively superseded in fundamental research by the start of the 1960s.

When ionising radiation (alpha or beta) passes through this chamber, it ionises the surrounding vapour. This causes the vapour to condense about that location, due to the vapours’ supersaturated state. The trails are formed by the continued propagation of ionising radiation through the chamber, as they have high energy. The trails are characteristic to the form of radiation. For example, alpha particles have broad, straight paths while beta particles have thinner tracks and are more easily deflected. This is due to their mass and charge – alpha particles are more highly charged than beta particles, so they affect the vapour in a larger range (thicker tracks). They are also more massive and thus are deflected less easily than electrons (electrons’ path bends due to collisions). Alpha particles, which are relatively heavy, will produce straight dense trails (below, left). Beta particles are light and leave wispy, irregular trails (below, center). When there is no radiation source, cosmic rays may enter the chamber, producing thin misty trails (below, right).

Magnetic fields can also be applied to study the movement of these particles, as they are charged. Alpha and beta particles will curve in the opposite directions. Gamma rays do not produce readily visible tracks because they do not interact strongly with matter (do not ionise atoms readily).

• See attachments discuss Pauli’s suggestion

of the existence of neutrino and relate it to the need to account for the energy distribution of electrons emitted in β-decay

When alpha particles are emitted from a source they have the exact same energies no matter what. However, it was noted by physicists that beta particles were often emitted with varying energies, even though they were from the same source. There was also debate as to whether the energies were continuous or line spectra, as equipment was not sufficiently sensitive.

It was established by Chadwick (using a Geiger ‘point counter’ to detect beta particles) that they had continuos spectra, using an apparatus similar to shown below.

so

Even though these beta particles were emitted from the same source under the same conditions they had differing amounts of energy, especially as both decays produced the same nucleus. In an attempt to resolve these problems, Pauli suggested the existence of another sub-atomic particle, which accompanied beta decay and could account for the varying levels of energy. The neutrino postulated Wolfgang Pauli to preserve conservation of energy, conservation of momentum, and conservation of angular momentum in beta decay, the decay of a neutron into a proton, an electron and an (now known as) antineutrino. Pauli theorized that an undetected particle was carrying away the observed difference between the energy, momentum, and angular momentum of the initial and final particles. This particle would be very penetrating, extremely difficult to detect, and be neutral. The existence or otherwise of this particle could not be established, but later on Fermi was able to explain beta decay, through his famous paper. He applied Pauli’s suggestion of a new particle and deduced its properties. • They have either zero or very small mass • They are neutral • They travel close to the speed of light (if they have mass) or at the speed of

light, if they are massless • They possess both momentum and energy (accounting for the differing

energies of electrons in beta decay) • They have an intrinsic spin • They have very high penetrating power and interact very little with matter

beta-minus decay

beta-plus decay

Eventually the neutrino was detected through inverse beta decay – that is,

A proton would interact with an antineutrino to form a neutron and a positron. Cowan and Reines detected the presence of these antineutrinos with this method. As such, the presence of antineutrinos and hence neutrinos in general was confirmed.

evaluate the relative contributions of electrostatic and gravitational forces between nucleons

account for the need for the strong nuclear force and describe its properties

The nuclei of atoms are obviously held together by attractive forces as they don’t spontaneously fly apart. Scientists originally thought that the force of gravity between nucleons would balance the electrostatic repulsion. However, we shall calculate the magnitude of the forces which protons and neutrons experience in the nucleus.

Calculate the forces between two protons

Thus the magnitude of electrostatic repulsion between two protons is much greater than the attractive force of gravity by magnitude of around 1036

Clearly the attractive force of gravity is much smaller than the repulsive force of electrostatics (even if we take into account the extra attractive force from the presence of uncharged neutrons). This would result in nuclei spontaneously flying apart, except that this does not occur in nature. Thus there must be another force (stronger than electrostatic repulsion) which holds the nuclei together. This force is known as the strong nuclear force. The properties of this strong nuclear force: • It is independent of charge, and acts between nucleons (protons and

neutrons). • At normal internucleon distances, it is a very strong attractive force (much

more than the electrostatic repulsion). However at very small distances (less than the diameter of the nucleon, about 0.4 fm) it changes from an attractive to repulsive force. Also, the Coulomb force between protons has a much larger range and becomes the only significant force between protons when their separation exceeds about 2.5 fm.

• It acts over a small range only (~10-15m) and its strength rapidly decreases after this. Proton repulsion occurs between each proton in a nucleus but the strong nuclear force only acts between adjacent nucleons.

• It prefers to bind pairs of nucleons with opposite spin, and pairs of pairs

whose spin is each zero (e.g. alpha particle is exceptionally stable). • The exchange particle associated with the strong nuclear force is the pi

meson, which has mass (thus it ‘works’ over a short distance only while the massless photon allows the electromagnetic force to extend infinitely)

explain the concept of a mass defect using Einstein’s equivalence between mass and energy

* solve problems and

It was noted that the sum of the individual masses of nucleons was greater than whole – that is, some mass appeared to be missing from the complete nucleus. For example, a deuterium ion has a mass of 2.014102 u while the mass of a proton and neutron is 2.01649 u. Thus, it appears to be missing a mass of 0.002388 u. This missing mass can be converted into a value for energy, by E=mc2. In this case, the binding energy is 2.224 MeV.

analyse information to calculate the mass defect and energy released in natural transmutation and fission reactions

This is known as the binding energy, and it is the energy which holds the nucleus of an atom together. It comes from the mass defect of atoms. To break the nucleus apart, we would need to supply an amount of energy greater than the binding energy. It also means that if we were to combine a proton and neutron to form deuterium, then 2.224 MeV of energy would be released. We can also analyse the binding energy per nucleon by taking the total binding energy and dividing it by the total number of neutrons and protons combined. It is this concept of binding energy and mass defect which allows for energy changes in nuclear reactions. To release energy, we would combine or split nuclei in such a way that the mass of the products would be less than the mass of the reactants, such that energy would be released. The only way that this mass would be less would have to be accounted for by the concept of mass defect – as the numbers of nucleons is conserved. A practical example:

The atomic masses:

139La 138.8061 u 1n 1.008665 u 95Mo 94.9057 u 1p 1.007276 u 235U 235.0439 u 0e 0.00054858 u

The mass deficit of the products relative to reactants is 0.3196 u. This means that the energy released in the nuclear reaction is 297.7 MeV.

From this graph we note that either splitting high-mass nuclei or fusing lighter nuclei will increase the binding energy per nucleon. This means that energy is released to the environment. Nuclear energy is based on this concept.

• Skill describe Fermi’s initial

experimental observation of nuclear fission

Nuclear fission is the process in which a heavy unstable nucleus splits to form two lighter nuclei, each of which are more stable. Fermi observed nuclear fission first, but these results were initially not understood and were only interpreted correctly years later. Fermi bombarded atoms of uranium with neutrons and assumed that the product was the element 93, because beta radiation was detected. While this would be true for U-238, Fermi’s sample had excess U-235 and from this some nuclear fission occurred. It was noted that the experiment, when performed in different parts of the room, had differing results. Noticeably, activity was greater when the substance being irradiated was left on a wooden rather than marble table. To further test this, Fermi intended to use a block of lead between the neutron source and the target – but at the last moment switched it for paraffin. This greatly increased the intensity of radiation and thus Fermi discovered why slow neutrons are better than fast neutrons at irradiation (they spend more time in the vicinity of the nucleus and are thus more easily captured). Later on, Hahn would perform the experiment and Meitner would correctly identify the process as fission. From this it was realised that much energy could be extracted from nuclear fission.

describe Fermi’s demonstration of a controlled nuclear chain reaction in 1942

Fermi created the first artificial nuclear reactor (atomic pile, named the Chicago Pile-1) in 1942 as part of a demonstration of the viability of nuclear reactions as an energy source. He aimed to show that a nuclear reactor could be self-sustaining. His atomic pile consisted of 50 tonnes of natural uranium in 22,000 slugs, and dispersed through 400 tonnes of graphite (as 40,000 graphite bricks). Graphite was chosen as the moderator because it was the only one available in sufficient purity. It contained critical mass of the fissile material, together with control rods, and was built as a part of Manhattan Project research. The controls consisted of cadmium-coated rods that absorbed neutrons. Withdrawing the rods would increase neutron activity in the pile to lead to a self-sustaining chain reaction. Re-inserting the rods would dampen the reaction. The test occurred on December 2 1942. Initially many control rods were inserted into the pile. They would be slowly withdrawn until a self-sustaining reaction was reached. 9:45 am The control rods began to be slowly withdrawn, with Fermi

performing calculations from the trace on the chart recorder. 11:45 am The automatic control rod, set at a too-low level, was set off. A

break for lunch was then called. 2:00 pm The process resumed. 3:25 pm Fermi predicted that the trace would not level off and a few

minutes later the reaction became self-sustaining. It stayed that way for 28 minutes, after which it was dampened by reinserting the control rods.

compare requirements for controlled and uncontrolled nuclear chain reactions

Nuclear fission is known to require one neutron only, and yet in the process of splitting several neutrons are emitted. For example,

These two possible decay chains produce more neutrons than they require. Also, each fission produces a large amount of energy.

If a sample of uranium is irradiated, then for each uranium atom split, three more are split after that. An uncontrolled nuclear reaction involves a nuclear reaction which progresses exponentially as the rate of reaction increases with each step. This occurs when the excess neutrons from the fission are free to propagate further fissions. As each fission releases energy, an uncontrolled reaction would release enormous amounts of energy in a short amount of time. This is useful in applications such as nuclear bombs as the large amount of energy can be put to

destructive use. To create an uncontrolled reaction we need a critical mass of fissile material – that is, material of sufficient density to sustain a chain reaction with a ratio of exit:input neutrons of greater than 1:1. Also, for use in bombs, this material needs to be subcritical during transport but be able to go critical at will. Some examples of nuclear bombs and uncontrolled chain reactions are explored later on. In controlled reactions, however, the number of emitted neutrons is controlled such that each fission results (on average) in only one other fission. For example:

As such, the reaction has exactly a 1:1 ratio and produces a steady stream of energy. These types of reaction are used in nuclear reactors today, extracting energy at a steady rate. They control the reaction by absorbing excess neutrons with control rods and ensuring that neutrons cause fission with moderators (these slow neutrons down to fissile speeds). These control rods can be moved in or out depending on how much the reaction needs to be slowed down. See below point on principles of nuclear reactors. If the neutrons are absorbed too readily, however, the ratio dips below 1:1 and the nuclear chain reaction dies out quickly. This is not productive.

4. explain the basic principles of a fission reactor

Fuel: • fissionable material used (e.g. U-235) as source of neutrons • need critical mass to create self-sustaining reaction • usually present as fuel rods to allow easy insertion and removal Regulation: • moderators used to slow neutrons down for easier capture (thermal neutrons)

-> the moderator is made of a material which does not absorb them but slows them down (e.g. heavy water, graphite, normal water bad as it absorbs neutrons itself to make heavy water)

• can be alternating such that a neutron from one fuel rod passes through moderator then goes into another fuel rod

• fission reaction controlled to allow only one neutron from fission reaction to cause further fission -> others are absorbed by control rods (material absorbs neutrons without fission, e.g. cadmium) to prevent nuclear explosion

• in event of emergency excess control rods can be dropped down under gravity to dampen reaction

Energy use: • heat energy from reaction form kinetic energy of fission is removed by a

coolant (e.g. heavy water, Na(l), CO2) which is used for work (e.g. pressurized steam to drive turbines)

• this coolant needs to exchange heat with another coolant as it is radioactive Shielding: • enormous amounts of radiation produced from nuclear fission, so radiation

shields needed • reflect escaping neutrons back into core, protecting walls from damage

(graphite and lead) • protect workers from harmful gamma radiation (shield of thick concrete

absorbs radiation) describe some medical

and industrial applications of radio-isotopes

* identify data sources, and gather, process, and analyse information to describe the use of: • a named isotope in

medicine • a named isotope in

agriculture • a named isotope in

engineering

Radio-isotopes are useful in many areas, such as medicine, agriculture and engineering. Medicine: Iodine-123 is also used to study and treat thyroid disorders, as the thyroid gland is the only major user of iodine in the body, which uses it to produce the hormone thyroxin. It is a beta and gamma radiator, with a relatively safe half-life of 13 hours. After a drink of radioactive NaI or a capsule, the patient’s iodine uptake is measured, and compared to healthy iodine uptake levels within a few hours. A different value to this could indicate a malfunction. This difference can be analyzed by a doctor to determine whether there exists a possibility for thyroid cancer. Larger doses of I-131 can be used for radiation therapy to treat tumours in the thyroid. Industry: The use of radioisotopes in industry includes those in agriculture and engineering. • Agriculture: Phosphorus-32 is often used as a tracer in plants to track the movement of nutrients, especially useful when tracking the uptake of fertilisers. P-32 is a beta emitter with a half-life of 14.3 days and P-32 can be incorporated chemically as part of fertilisers and weed-killers, and radiation detectors can monitor the amount of chemical inside the plant, as opposed to that administered dose. Phosphorus is important to plant growth and the half-life of 14.3 days is on a good time scale to study chemical uptake. It allows farmers and agriculturalists to optimise the production and use of fertilisers and weedicides, saving money and optimising production. • Engineering: The penetrating power of γ radiation allows it to detect faults in metals due to metal fatigue, hairline cracks, or poor welding. More γ radiation passes through areas with less thickness, and this method is used on pipelines, boiler welds, and metal fatigue in aircraft. Radioisotopes (e.g. Co-60, Sr-90) are convenient for this purpose as they can be inserted without dismantling. Co-60 is used because it is an emitter of gamma rays which will penetrate metal parts. It has a half-life of 5.3 years and can be used in a chemically inert form held inside a sealed container. This enables the equipment to have a long lifetime and not require regular maintenance, leading to lower costs and higher efficiency.

describe how neutron scattering is used as a probe by referring to the properties of neutrons

Neutrons can be effectively used as a probe to study the structure and properties of matter. They are produced from a nuclear reactor. The main tools for neutron analysis of matter are the spectrometer and diffractometer. Neutrons have a number of properties which make them useful: • The neutron has a wave nature, and the de Broglie wavelength of thermal

neutrons is comparable to the spaces between atoms. This allows interference patterns to be formed as the lattice acts as a diffraction grating.

• The neutron has a magnetic moment, which allows it to be used to study materials or structures with magnetic properties.

• Neutrons interact strongly with nuclei of atoms, which allows them to be used as a probe to study the structure of nuclei, especially different isotopes of the same element.

• The neutron has similar vibrational energies to atoms in solids and liquids and as such can be used to study the movement of atoms in molecules.

• Neutrons can be used to study matter non-destructively. Thus scientists can use neutrons to study the structure of matter effectively.

identify ways by which physicists continue to develop their understanding of matter, using accelerators as a probe to investigate the structure of matter

Physicists can develop their understanding of the structure of matter through probing the nucleus with particle accelerators as well as neutrons (discussed above). A particle accelerator is a device that uses electric fields to propel electrically-charged particles to high speeds and to contain them. Accelerators give high energy to subatomic particles, which then collide with targets. Beams of high-energy particles are useful for both fundamental and applied research in the sciences. For the most basic inquiries into the dynamics and structure of matter, space, and time, physicists seek the simplest kinds of interactions at the highest possible energies. Out of the collisions and interactions come many other subatomic particles that pass into detectors. From the information gathered in the detectors, physicists can determine properties of the particles and their interactions. Some examples of these particle accelerators can be: • Linear Accelerator

Linear accelerators consist of an alternating power supply connected to a series of lengthening tubes. The changing electric field is setup such that the particles are accelerated down to a target. Initially the ion source has an opposite charge to the nearest tube, and is accelerated towards it. As the particle travels through the tube and exits it, the polarity changes such that the tube behind the particle repels it and the tube ahead attracts it. This continues on, and each tube must increase because the period between frequency changes remains constant while the speed increases. As such, the particle can be accelerated to very high velocities. However, one disadvantage of these is the sheer length required to attain sufficiently high velocities. • Cyclotron

A cyclotron accelerates charged particles through the dees. A magnetic field exists going through the page such that the particles are subject to a force perpendicular to their direction of motion. This causes circular motion. The electric field is set up such that the dees have alternating charge, and the particle accelerates as it moves between the dees (the radius increases due to speed increase). Eventually the particle is accelerated to high speeds and exits

the cyclotron. • Synchotron Synchotrons are the main type of accelerator used today. A radio frequency electric field is used to accelerate the particles around a circuit of constant diameter, providing a kick. A steadily strengthening magnetic field keeps these particles moving in a constant diameter. They require less energy to run, but a disadvantage is that only one batch of particles can be accelerated at a time.

discuss the key features and components of the standard model of matter, including quarks and leptons

The standard model of matter consists of a number of aspects, each of which should be mentioned in exams. It was developed to explain subatomic particles using interactions and classes of particles, as many had been discovered and was beginning to be difficult to keep track of (especially interactions). It is a mathematical description of the particles, their kinematics, and the interactions between them (reducing this to several laws). The types of particles involved are:

Hadrons particles affected by strong nuclear force Baryons hadrons with half-integer spin (e.g. proton, neutron) (3 quarks) Mesons hadrons with zero or integer spins (quark and antiquark)

Fermions particles obeying Pauli exclusion principle with half integer spin Leptons particles not experiencing strong nuclear force, and half-integer spin (e.g.

electron)

Quark quarks carry colour charge and interact via the strong force. Bosons force-carrying particles (photons, gluons, gravitons)

• There are six accepted types (flavours) of quark and six flavours of lepton, both of which are elementary particles.

• Protons consist of uud quarks and neutrons are made of ddu quarks. • Baryons are made of 3 quarks, and mesons are made of a quark and an

antiquark. Lepton Quark Generation Name Charge Name Symbol Charge

electron neutrino 0 up u +2/3 1 electron -1 down d -1/3 muon neutrino 0 charm c +2/3 2 muon -1 strange s -1/3 tau neutrino 0

top t +2/3 3 tau -1 bottom b -1/3

The Standard Model predicted the existence of W and Z bosons, the gluon, the top quark and the charm quark before these particles had been observed. Their predicted properties were experimentally confirmed with good precision. The model also deals with force-mediating particles. It suggests that all the fundamental forces result from the exchange of these force mediating particles between the matter particles.

electromagnetic photon weak nuclear force various bosons strong nuclear gluon gravity graviton?

However the force carrying-particle for gravity is undiscovered. This remains a problem with the model. Shortcomings • incompatible with gravity and general theory of relativity • provides no reasoning for numbers (e.g. 6 quarks, 6 leptons) • cannot explain masses cannot explain whether there are more fundamental particles (e.g. leptoquark?)

* gather, process and analyse information to assess the significance of the Manhattan Project to society

Outline: • Code name for US project to develop atomic bomb • German scientists had discovered nuclear fission, raising possibility of nuclear

bomb, so America began its own project • Japan caused America to enter the war • Fermi demonstrated nuclear reactor in 1942, and by 1945 some bombs were

made and two were dropped

Two subcritical masses of nearly pure U-235 are separated. Detonation of the explosive charge forces the two masses together at high speeds. This is now super-critical and a nuclear explosion occurs.

A slightly subcritical mass of Pu-239 is surrounded by a shell of explosives. These are triggered, compressing the plutonium into critical density. This creates a nuclear explosion.

Positive Impacts

• conclusion of WWII • greater understanding of nuclear energy • invention of nuclear power plants to produce energy • application of nuclear physics to medicine, industry and agriculture for benefit

of all Negative Impacts • the bombs were very expensive to develop (leading to questions of legitimacy

of these expenditures) • enabled USA not USSR to control postwar policy by eliminating Japan • some scientists objects to its use, staining America’s reputation • beginning the arms race (Cold War), expending large amounts of money

which can be used elsewhere • excess of nuclear weapons being developed • led to development of even more powerful, destructive weapons • mass annihilation of people at Nagasaki and Hiroshima • nuclear fallout from testing sites and drop zones, leading to mutations • ethical dilemmas raised about nuclear research