Topic : Quanta to Quarks

Notes for Quanta to Quarks

Below are the dot points of Quanta to Quarks. Click on the dot point to expand relvant information. These notes were written by; Steven Zhang Click here to donate him

Models of the Atom

  • Discuss the structure of the Rutherford model of the atom, the existence of the nucleus and the electron orbits

J. J. Thomson’s Model

The discovery of electrons by Thomson had changed the view on indivisibility of atoms. Thomson was able to determine the charge and mass of electrons and the mass of the electron was found to be 1800 times lighter than the lightest atom, Hydrogen. He concluded that electrons are sub-atomic. He proposed a crude model of the atom, known as the plum-pudding model. Negative electrons are like plums in the positive pudding.

Ernest Rutherford’s Alpha Particle Scattering Experiment

  • In 1911 Geiger and Marsden, at the instigation of Rutherford, performed an experiment in which the newly discovered positively charged alpha particles were fired at a thin gold foil.
  • It was observed that most of the alpha particles passed through with only small deflections (as expected with the Thomson model of the atom of the time).
  • However it was found that about 1 in 8000 alpha particles deflected back at angles greater than 90°! From this result, Rutherford proposed that the only way that the alpha particles could be deflected through large angles is if all the atom’s positive charge and nearly all its mass wasConcentrated in a small dense nucleus with the electrons some distance away
  • From the results of the alpha particle scattering experiment, Rutherford was able to show that the atom is mostly empty space and was able to estimate the size of the atom and its nucleus.
  • He proposed a model where orbiting electrons were held to the positive nucleus by electrostatic attraction. This model was criticised as the physics knowledge of the time suggested an orbiting electron would emit electromagnetic radiation and spiral into the nucleus.

Inadequacies of Rutherford’s Atom

Although Rutherford’s model successfully explained alpha particle scattering, it left many questions unanswered:

  • What is the nucleus made of?
  • What keeps the negative electrons from being attracted into the positive nucleus?
  • How are the electrons arranged around the nucleus?

  • Analyse the significance of the hydrogen spectrum in the development of Bohr’s model of the atom

Niels Bohr’s Model of the Atom Bohr uses Quantum Theory to Explain the Spectrum of Hydrogen: Bohr knew that, somehow, atoms must produce radiation that formed a characteristic spectrumfor each element. Bohr realised that the “atomic oscillators” of Planck were probably electrons in the atom. The Rutherford model failed to provide any information about the radius of the atom or the orbital frequencies of the electrons.

Bohr was introduced to Balmer’s equation for the wavelengths of the spectral lines of hydrogen (more on this later), a purely empirical formula at the time. After seeing this equation, Bohr realised how electrons were arranged in the hydrogen atom and also how quantum ideas could be introduced to the atom.

  • Discuss Planck’s contribution to the concept of quantised energy

Recall: Planck, Einstein and “Quantised Energy” Planck interpreted his black body result as meaning that the “atomic oscillators” that produced the radiation could vibrate only with certain discrete amounts of energy, quanta. Einstein later extended this idea to the radiation itself being quantised, photons.

  • Define Bohr’s postulates

Bohr’s Postulates

In 1913, Bohr published three papers that addressed the problem of electrons in the Rutherford  model and pointed out that the accelerating electrons must lose energy by radiation and collapse into the nucleus. He then applied quantum theory to the atom. To account for the discrepancies between the Rutherford model of the atom and available experimental evidence in particular, the emission spectrum of hydrogen, Bohr proposed three postulates:

  1. Electrons in an atom exist in “stationary states” in which they possess an unexplainable stability. These states correspond to certain allowed orbits that allow electrons to revolve without radiating energy
  2. When an electron falls from a higher energy level to a lower energy level, it emits energy that is quantised by the Planck relationship E2 – E1 = ΔE = h f
  3. Angular momentum (mvr) is quantised and can only take values of nh/2n where n is the principle quantum number.

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

The Bohr Model and the Balmer Series One of the greatest successes of the Bohr model was that it was able to provide a physical basis for the Balmer series formula (which up until that point was purely an empirical formula). Bohr’s reasoning was as follows:

The Hydrogen Atom Explained We are now able to calculate the wavelengths of the many spectral lines of the hydrogen atom. The original series of the spectral lines was known as the Balmer series and contained the four spectral lines in the visible region of the spectrum. These lines correspond to electron jumps to the second lowest energy state, or first excited state, (n = 2) of the hydrogen atom. Balmer’s formula allowed for speculation of the existence of other line series for hydrogen. These were later detected using spectroscopes.

  • Discuss the limitations of the Bohr model of the hydrogen atom

Limitations of the Bohr Model

The Bohr model takes the first step to introduce quantum theory to the hydrogen atom, but has the following limitations:

  • Multi-Electron Atoms: The Bohr model works reasonably well for atoms with one electron in their outer shell but does not work for any others. It is not possible to calculate the wavelengths of the spectral lines of all other atoms.
  • Relative Intensities of Spectral Lines: Examination of spectra shows that the spectral lines are not of equal intensity but the Bohr model does not explain why some electron transitions would be favoured over others.
  • Hyperfine Lines: Careful observations with better instruments showed that there were other lines known as the hyperfine lines. There must be some splitting of the energy levels of the Bohr atom but the Bohr model cannot account for this.
  • Zeeman Effect: When a gas is excited while in a magnetic field, the emission spectrumproduced shows a splitting of the spectral lines (called the Zeeman effect). Again, the Bohr model cannot account for this
  • Ad hoc Mixture of Classical and Quantum Physics: Finally, the Bohr model is a mixture of classical physics and quantum physics and this, in itself, is a problem.

Quantum Physics

  • Describe the impact of De Broglie’s proposal that any kind of particle has both wave and particle properties

Louis De Broglie’s Proposal In 1923, de Broglie argued that the fact that nobody had managed to perform an experiment that settled once and for all whether light was a wave or a particle was because the two kinds of behaviour are inextricably linked – he made the bold proposal that all particles must have a wave nature as well as a particle nature. The expressions for the energy and momentum of light quanta have quantities that are properties of particles on the left-hand side and quantities that are properties of waves on the right-hand side:

Electrons had been thought of as well-behaved particles except for the fact that they occupied distinct energy states in the hydrogen atom. These energy states were associated with integers. De Broglie was aware of other phenomena in physics that were associated with integers. These included the interference of waves and the vibration of standing waves. He stated: “This fact suggested to me the idea that electrons, too, could not be regarded simply as corpuscles, but that periodicity must be assigned to them.” De Broglie described how matter waves ought to behave and suggested ways that they could be observed. The wavelength of a photon was Planck’s constant divided by its momentum and de Broglie proposed that, similarly, the wavelength of a moving particle would be Planck’s constant divided by its momentum. Therefore, photon momentum would be:

  • Describe the confirmation of De Broglie’s proposal by Davisson and Germer

Confirmation of de Broglie’s Proposal by Clinton Davisson and Lester Germer In 1923, Davisson and Germer proved the wave nature of matter by observing some characteristics of wave properties such as diffraction. Davisson and Germer scattered electrons from the surface of a nickel crystal and obtained an intensity pattern of the reflected electrons that showed diffraction effects. This proves that electrons of particle nature also have wave characteristics

  • Explain the stability of the electron orbits in the Bohr atom using De Broglie’s hypothesis

Bohr’s Stable Electron Orbits Explained When de Broglie developed the idea of matter waves, he had believed that the orbits of the electron in the hydrogen atom were something like standing waves. The condition for a standing wave to form on a string fixed at each end is that the length of the string must be an integral number of half-lengths. If we consider an electron as setting up a standing wave pattern as it orbits around a nucleus, there must be an integral number of wavelengths in that pattern. If the circumference is taken as 2πr then there are n wavelengths in the circumference, nλ = 2πr. From this, and the de Broglie wavelength:

The Electron Microscope

  • Outline the application of the wave characteristics of electrons in the electron microscope

Electron Microscopes Because electrons have a much smaller wavelength than light, they produce much less diffraction than light. The diffraction effects of electrons in an electron microscope are therefore much smaller than those of light in an optical microscope. Electrons, therefore, have a much better resolving power than light and electron microscopes makes use of this reduced diffraction to produce images which are of much higher magnification than is possible with light.

Electron microscopes do not take advantage of the wave nature of electrons to focus the electrons. In the ‘lenses’ of an electron microscope it is the particle nature of electrons that is important. Electrons are focused by deflection by electric or magnetic fields. The forces that produce this deflection depend on the particle nature of the electrons.

In all electron microscopes:

  • An electron source produces a stream of electrons that are accelerated towards the specimen by an accelerating potential difference.
  • Metal apertures and magnetic lenses confine and focus the electron beam.
  • Othe magnetic lenses focus the beam on the specimen.
  • Interactions inside the specimen affect the electron beam. These effects are converted intoan image.

Because air will deflect electrons, the interior of electron microscopes is under a high vacuum which means that the specimens must be dead – a definite disadvantage to light microscopes. However, electron microscopes can magnify up to a million times, which is a major advantage.

  • Discuss the relationships in electron microscopes between the electrons, magnetic lenses and refraction

Magnetic Lenses

Recall that a charge particle moving in a magnetic field experiences a force. By passing an electron beam through a set of high-powered magnets, the beam can be focussed.

Electromagnetic lenses consist of a solenoid with magnetic pole refraction pieces that concentrate and determine the shape of the field.

In optical microscopes the glass lenses have a fixed focus and the specimen is moved towards or away from the objective lens to bring it into focus. In electron microscopes, the electromagnetic lenses have a variable focus and the specimen to objective distance is kept constant.

Magnification is achieved by varying the current in the objective lens coil.

Types of Electron Microscopes The early electron microscopes were transmission electron microscope types (TEM) in which the electrons passed through the specimen. They are analogous to transmission light microscopes.

A later development (1942) was the scanning electron microscope (SEM) which can produce a three-dimensional image of the specimen by reflection of the electrons off the specimen. These are analogous to reflecting light microscopes.

Applications of Radioactivity

  • Identify the importance of conservation laws to Chadwick’s discovery of the neutron

The Conservation Laws which apply to Atoms There are a number of quantities in chemical and nuclear changes, which, in total remain unchanged throughout the process.

Charge is Conserved (Atomic Number Z) During a nuclear or chemical reaction, the total charge of all the reactants equals the total charge of all the products

Mass Number A is Conserved

The total number of protons + neutrons remains the same during a reaction.

Mass / Energy is Conserved

The total mass or energy equivalence of mass (by E = mc2) during a reaction remains the same. This means during a nuclear reaction, mass / energy cannot be created or destroyed.

James Chadwick discovers the Neutron

In 1930, the Germans Walther Bothe and Becker discovered that bombarding beryllium with alpha particles resulted in the emission of a penetrating type of radiation. The radiation seemed to be similar to gamma rays but it was much more highly penetrating.

In France, Frederic Joliot and Irene Curie studied this radiation falling on a block of paraffin (paraffin is a hydrocarbon rich in hydrogen atoms). They found that the radiation knocked protons (hydrogen nuclei) from the paraffin. Now that charged particles were involved, it was much easier to determine their properties. The high energy of the protons emitted (5 MeV) was a problem because applying the conservation of energy and conservation of momentum to the collision between a gamma ray and a proton yielded a value for the incident gamma ray of at least 50 MeV. This was a major dilemma because the energy of the incident alpha particles was only about 5 MeV.

In 1932, Chadwick suggested that this radiation consisted of Rutherford’s neutrons and not gamma rays. By applying the laws of conservation of momentum and energy, Chadwick was able to prove the existence of the neutron:AB

  • Define the contents of the nucleus (protons and neutrons) as nucleons and contrast their properties

Nucleons are particles that normally reside in the nucleus. These are collectively protonsand neutrons.

  • Define the term ‘transmutation’

Transmutation Transmutation occurs when one element changes into another. In all transmutations, the mass number and atomic number are conserved.

  • Define Fermi’s experimental observation of nuclear fission and his demonstration of a nuclear chain reaction

Enrico Fermi Discovers Nuclear Fission

Between 1934 and 1938, Fermi bombarded many of the known elements as possible with the newly discovered neutrons. The neutron, because of its neutral nature, proved to be better at causing transmutations than alpha particles, which are repelled by the positive nucleus by their positive charge. In the majority of cases, new isotopes were formed. Occasionally this new nucleus was radioactive and emitted a beta particle.

When Fermi reached uranium (the heaviest known element, 92), it was hoped that the uranium would undergo beta decay to form an isotope of element number 93 – the first transuranic element.

Although this occurred, it was found that there were at least four different products which emitted betas with different measurable half-lives. What was eventually found was that uranium is a mixture of isotopes U-235, U-238 and U-233. The U-235 isotope was reacting, absorbing the neutron and forming an unstable isotope that split into two roughly equal halves – nuclear fission.

Fermi and Chain Reaction For the fission of U-235, it can be noted that more neutrons are produced than used. This opens the possibility of a single neutron causing a chain of atoms to react.

  • Identify that Pauli’s suggestion of the existence of neutrino is related to the need to account for the energy distribution of electrons emitted in β-Decay

Pauli and the Neutrino

All alpha particles emitted from a particular radioactive species have the same energy but beta particles seem to be emitted with a range of energies. There was considerable debate as to whether the beta particles had a continuous or line spectrum.

The question was asked, how could one beta decay be associated with emission of a certain amount of energy from a nucleus but another beta decay from a similar nucleus be associated with a different amount of energy? After all, both decays produced the same new nucleus.

In 1931, in an attempt to resolve the paradoxes involving beta decay, Pauli proposed that another particle, the neutrino, was emitted during beta decay.

Fermi proposed that the number of electrons and neutrinos was not constant. Electrons and neutrinos could be created or disappear just like photons. The assumption that another small neutral particle was forming allowed the sum of the particles on both sides of the equations to be equal in mass/energies.

  • Describe nuclear transmutations due to natural radioactivity
Artificial Transmutations Particles are fired into nuclei to make it unstable. This causes it to undergo a nuclear reaction (i.e. a transmutation) e.g. nuclear fission.

Nuclear Transmutations due to Natural Radioactivity

Natural transmutations occur in radioactive decay such as alpha and beta decay.

  • Evaluate the relative contributions of electrostatic and gravitational forces between nucleons

Forces Holding the Nuclear Together Protons in the nucleus should repel each other violently through coulombic repulsion.

  • Account for the need for the strong nuclear force and describe its properties

The Strong Nuclear Force The strong nuclear force exists between any two nucleons and acts against the electrostatic repulsion between protons. It is only strong at very close range ie. the protons and neutrons have to be very close together to attract. Otherwise the protons will repel. Overcoming this repulsive force before the nuclei are close enough to attract explains the difficulty in combining atoms (nuclear fusion).

Heavier nuclei need more neutrons to remain stable as they add extra strong nuclear force without adding extra electrostatic repulsion.

Mass Defect is the difference between the mass of a nucleus and the sum of the masses of its individual parts.

The existence of binding energy implies that the making of atomic nuclei from their particles causes a mass drop and emission of energy. The concept of binding energy has another aspect. Breaking an atom into its particles requires energy.

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

Binding Energy Per Nucleon This is a very good indicator of nuclear stability. Any nuclear reaction that produces daughter nuclei with higher BE/nucleon than the reactant has increased the total Be/nucleon, which means that energy is given off by the reaction. There are two types of reactions that do this:

  1. Nuclear fission of heavy nuclei
  2. Nuclear fusion of light nuclei

  • Compare requirements for a controlled and uncontrolled nuclear chain reaction

Controlled and Uncontrolled Chain Reactions

In a controlled chain reaction, only one neutron from each fission is available to split another uranium atom. Surplus neutrons are absorbed by control rods made of materials such as cadmium (that absorb neutrons without undergoing fission) to keep the rate of fission steady. In an uncontrolled chain reaction, each neutron released by the uranium atom as it splits is allowed to hit another uranium atom. There is a rapid build up of atoms undergoing fission and a rapid release of energy.

Nuclear Applications

  • Explain the basic principles of a fission reactor

Nuclear Fission Reactors Nuclear fission reactors for power stations are used as a heat source to boil water to produce pressurised steam to drive a turbine/dynamo to generate electricity.

Every reactor needs:

  • Fuel Rods – consist of fissionable material such as U-235 (most uranium is U-238)
  • Control Rods – absorb neutrons to slow down reaction rate (eg. cadmium or boron)
  • Moderator – slows down neutrons by collision (eg. heavy water, graphite). Fast neutrons are produced by the reactions but slow neutrons are more effective at triggering new reactions
  • Coolant – removes the heat produced by the reactor (to prevent fire) and to use it to boil water to produce the steam to drive the turbines
  • Criticality – a reactor must be a certain size before a controlled chain reaction is possible
  • Start Up – To produce fission, a source of neutrons is necessary. The best way is to use the Chadwick method and use Radium to bombard Beryllium with alphas to produce neutrons.

Once the reaction commences, fuel rods are loaded in one by one and control rods are drawn after each loading in an attempt to reach criticality.

  • Describe some medical and industrial applications of radio-isotopes

Applications of Radioisotopes Medical and industrial applications of radioisotopes include medical diagnosis by radioactive tracing, cancer treatment by radiotherapy, sterilisation, tracing, and attenuation.

  • Explain why neutron scattering is used as a probe by referring to the properties of neutrons

Neutron Scattering

Neutron scattering is a powerful method of analysing the internal structure and properties of matter using neutrons. Like all atomic particles, neutrons demonstrate wave characteristics and form diffraction patterns. Their particular value is found in their lack of charge. This allows them to penetrate atoms to a great degree than electrons or even X-rays. Neutron scattering works particularly well for materials containing light atoms such as hydrogen. This includes many organic substances. The technique aided the analysis and developments of better automobile exhaust catalysts, magnetic materials in computer data storage devices and new superconducting materials. It even helped in the study of pathogenic viruses.

The Structure of Matter

  • Identify the ways by which physicists continue to develop their understanding of matter, including:
    • The use of accelerators as a probe to investigate the structure of matter
    • The key features and components of the standard model of matter, including quarks and leptons
    • The links between high energy particle physics and cosmolog

Particle Accelerators Particle accelerators are one of the main tools used to create and measure the small particles thatmake up atoms. They act by accelerating charged particles to quite high speeds before smashing them into a target of atoms. The products often form tracks that can be photographed as they spiral around a cloud chamber and form other particles by radioactive decay. Linear Accelerators An electron, a proton, or a heavy-ion accelerator in which the paths of the particles accelerated are essentially straight lines rather than circles or spirals. Cyclotrons A circular particle accelerator in which charged subatomic particles generated at a central source are accelerated spirally outward in a plane perpendicular to a fixed magnetic field by an alternating electric field. A cyclotron is capable of generating particle energies between a few million and several tens of millions of electron volts. Synchrotrons An accelerator in which charged particles are accelerated around a fixed circular path by an electric field and held to the path by an increasing magnetic field.

The standard model has two main components to explain the fundamental forces:The electroweak theory: This describes interactions through the electromagnetic and weak forces. Quantum chromodynamics: This is the theory of the strong force. (Gravity is not part of the standard model.) T here are three families under which matter is grouped – quarks, leptons and bosons. Matter particles: These are fundamental particles. They are the quarks and leptons. Force-carrier particles: Each type of fundamental force is caused by the exchange of

There are three families under which matter is grouped – quarks, leptons and bosons. Matter particles: These are fundamental particles. They are the quarks and leptons. Force-carrier particles: Each type of fundamental force is caused by the exchange of forcecarrier particles. These are the fundamental (or gauge) bosons. They include phons and gluons.

Dark Matter Cosmology Research into astronomy has led to the prediction of “dark matter” as an important constituent of the universe. What is this dark matter? It seems as if it may be different from any matter we have experienced. Does it consist of so far undiscovered fundamental particles? If so, will they fit into the Standard Model?

Dark Energy astronomy? Another recent discovery from astronomy is that the universe is expanding at an increasing rate. The term “dark energy” has been applied to a type of matter, which has a repulsive rather than attractive gravitational force. Is the universe really expanding at an increased rate and if it is, what does that really mean in terms of matter in the universe? As research into the most fundamental aspects of matter developed, it became linked to research in cosmology and the origins of the universe. The important questions about the universe on a very large scale and on the very smallest scale are intertwined.