Topic 4: Quanta to Quarks

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

1/8000 were deflected back

Unexplained Phenomena: According to Maxwell, accelerating electrons emit electromagnetic radiation so the electrons should lose energy and spiral into the nucleus.

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

If gases at low pressure are excited by either intense heat or by applying a high voltage to a ‘gas discharge tube, then radiation is emitted only at discrete frequencies, producing a line spectrum rather than a continuous one.

If light with a continuous spectrum is passed through a gas, an absorption spectrum is produced, with inverted colour scheme

With Hydrogen’s spectrum, Rutherford’s model could not explain the spectral lines so another model (Bohr’s) was sought.

1.1.3 Define Bohr’s postulates

1. Electrons exist in fixed non-radiating orbits
2. Electrons only emit energy by ‘quantum jumps’ from one stationary state to another (producing discrete line emission spectra)
1. The radiated photon is equal to the difference in energy between one stationary state and the next (E2 - E1 = Change in E = hf)
1. Angular momentum (L = mvr) of electrons is quantised and can only take values of n(h/2pi) where n is an integer called quantum number.

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

• Planck solved the UV catastrophe by suggesting that the energy radiated and absorbed by a black body (a perfect absorber and emitter of radiation) was not continuous but rather quantised - it should be treated as packets of energy (photons). The energy could be described by E = hf

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

• When Bohr’s second postulate is combined with the expression for the energies of the stationary state the Rydberg Equation is able to be derived.

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

and

1.2.4 Analyse secondary information to identify the difficulties with the Rutherford-Bohr model

Failure to explain:

• Spectra of larger atoms
• Relative intensity of spectral lines
• Some lines appeared darker than others
• Existence of hyperfine spectral lines
• Many spectral lines consist of several closely spaced lines
• Zeeman effect
• The splitting of emission and absorption spectral lines by the application of an external magnetic field.
• Stark effect
• The splitting of emission and absorption spectral lines by the application of an external electric field.

1.2.1 Perform a first hand investigation to observe the visible components of the hydrogen spectrum

• Obtain a spectrometer
• Look through spectrometer at an excited hydrogen spectral tube
• Observe the spectra

1.2.2 Process and present diagrammatic information to illustrate Bohr’s explanation of the Balmer series

Balmer series refers to transitions from the 2nd energy level. (n = 2)

1.2.3 Solve problems using the Rydberg equation

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

• From p = hf/c he claimed that: "All matter has both particle and wavelike properties”
• He developed the idea mathematically, linking all mass with a wavelength known as matter waves.
• This wavelength can be found by:
• de Broglie's proposal revolutionised modern physics and gave birth to the new field of quantum physics.
• Quantum Physics was a field where the wave-particle duality of matter is focused on.
• This new field of physics attracted other major scientists, like Pauli, Heisenberg, Schrodinger, Dirac and others.
• These scientists developed a detailed theory known as quantum mechanics
• Quantum mechanics describes a set of physical laws that apply to objects smaller than the size of an atom.
• Also, it is shown later that De Broglie's allowed Bohr's stationary states to be adequately explained.

2.1.2 Define diffraction and identify that interference occurs between waves that have been diffracted

• Diffraction: waves are spread out as a result of passing through a narrow aperture, typically accompanied by interference between the waveforms produced.

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

• Davisson and Germer demonstrated that electrons in an electron beam are diffracted and produced a similar interference pattern to that produced by x-rays when they were scattered by a small crystal of nickel.
• Pattern produced by changing electron speed at a fixed angle
• The interference pattern of maxima and minima was consistent with the electrons behaving as if they were waves with a wavelength related to their momentum.
• Verified de Broglie’s proposal

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

• De Broglie’s proposal meant that each electron orbit in an atom could be treated like a standing wave that closes in on itself
• If a whole number of wavelengths fit into the circumference of the orbit, the standing wave will be maintained. (2πr=nλ)

2.2.1 Solve problems and analyse information using

2.2.2 Assess the contribution made by Heisenberg and Pauli to the development of atomic theory

And

3.1.6 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 beta decay

Heisenberg:

• Develops matrix mechanics
• Heisenberg uncertainty principle
• Position and momentum of a particle cannot be simultaneously measured with high precision
• Arises from the wave particle nature of matter
• Places limits on what we can know about the universe

Pauli:

• Pauli exclusion principle
• No 2 electrons may occupy the same quantum state at the same time
• Explains why electrons don’t go to ground state and why different elements have different arrangements
• Existence of the neutrino
• Explains the kinetic spectrum of energies produced by beta decay
• Additional particle in eleastic scattering so that momentum and kinetic energy is convserved
• Pauli proposed a chargeless, near massless particle must be carrying additional energy away.

3.1.1 Define the components of the nucleus (protons and neutrons) as nucleons and contrast their properties

Nucleons: Particles that make up the nucleus (i.e. protons and neutrons)

3.1.2 Discuss the importance of conservation laws to Chadwick’s discovery of the neutron

• In 1930, German scientist Walther Bothe noted that when beryllium was bombarded with alpha particles, a neutral but highly penetrative radiation could be obtained.
• In 1932, Englishman James Chadwick proposed that the unknown radiation was in fact made up of neutrons.
• The neutral charge was demonstrated as it was not deflected by electric or B-fields.
• He set out an experiment to study this unknown radiation.
• He directed the neutrons produced towards a block of paraffin wax
• Paraffin wax is rich in hydrogen atoms (protons) so the neutrons should have a good chance of colliding with those protons and knocking them out.
• As a result, protons were ejected from the wax and measured by the detector.
• By applying the law of conservation of momentum and law of COE, Chadwick was able to conclude the mass of neutrons was similar to that of a proton.
• Chadwick measured the recoil of the nuclei of hydrogen and nitrogen atoms after interacting with the natural radiation.
• The existence of neutrons was experimentally shown by Chadwick without directly observing them but done through demonstrating neutrons’ properties.
• Neutrons are difficult to assess as they have no charge and thus cannot be manipulated easily.

3.1.3 Define the term ‘transmutation’

Transmutation: Any transformation of the nucleus (any nuclear reaction)

3.1.4 Describe nuclear transmutations due to natural radioactivity

Alpha: Large number of protons and neutrons emits an alpha particle

Beta +: Neutron decays to create a proton and an electron and a neutrino

Beta -:

Gamma:  Transmutation Nucleus can be in an excited state and emits a photon and drops to a lower E state.

3.1.5 Describe Fermi’s initial experimental observation of nuclear fission

When Fermi bombarded Uranium -235 with neutrons he was puzzled when he found many unidentified products were produced (before he had only seen nuclear fusion which produced transuranic elements).

• They were all beta emitter with different half lives.
• This indicated another process (nuclear fission) must be taking place at the same time.

3.1.6 Discuss Pauli’s suggestion of the existence of the neutrino and relate it to the need to account for the energy distribution of electrons emitted in beta decay

Neutrino existence was suggested because in beta decay nuclear reactions:

• Energy
• Linear momentum
• Angular momentum
• All didn’t add up as expected by the conservation laws

To explain this missing energy Pauli proposed the existence of a new particle that

• Travelled at the speed of light
• Have no charge
• Interacts weakly with matter and is difficult to detect

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

and

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

The electrostatic force is way stronger than the gravitational force inside the nucleus so there must be a stronger force.

Properties:

• Independent of charge
• Acts between any nucleons
• Very attractive force much stronger than electrostatic propulsion
• Very short range force
• Only 10-15m - basically only between adjacent nucleons.

Force                                        Strength                                Range

 Gravitational Weak attractive force between nucleons Long Electrostatic Strong repulsive force between protons Long Nuclear Force Strong attractive Very short

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

Nuclear Binding Energy: Energy required to disassemble a nucleus into free unbounded neutrons and protons.

E=MC2 states that an energy has a mass

• Charged battery is heavier than uncharged
• Rock at bottom of a hill has less mass
• Projectile gains mass slightly as it escapes earth’s gravitational potential

Because the nucleons in a nucleus are attracted to each other they are at a lower potential energy together than when they are apart.

• When a nucleus forms, energy is lost therefore mass is lost
• To remove you have to give energy → give mass

The mass of any nucleus is smaller than the sum of the masses of its constituent protons and neutrons

Mass Defect: Sum of parts of proton and neutrons - measured mass of nucleus

Binding Energy = Mass defect x c2

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

• In 1942, Fermi constructed the first man-made nuclear fission reactor in a Chicago Uni Squash court.
• Fermi aimed to create a reactor in which the neutron multiplication factor (k) is greater than 1.
• This would allow a chain reaction to occur.
• In order to achieve this, Fermi built an atomic pile using layers of graphite blocks containing slugs of uranium metal and uranium oxide, alternated with layers of solid graphite blocks as moderators.
• Control rods of cadmium, known to be good neutron absorbers were inserted into the atomic pile amongst the uranium and graphite blocks to control the reaction.
• As the control rods were removed/withdrawn, the radiation produced was measured by a Geiger Counter.
• He then reinserted the cadmium rods to halt the nuclear reactions.
• His ability to start, maintain and stop a nuclear fission reaction demonstrated a controlled nuclear reaction.

3.1.11 Compare requirements for controlled and uncontrolled nuclear chain reactions

Criticality Factor (K) - Reproduction Factor

•  = average number of neutrons per fission that cause another fission
• K < 1 -- subcritical (reaction dies out)
• K = 1 -- critical (reaction can sustain itself)
• K > 1 -- supercritical (runaway)

Control rods suck out all the neutrons to control the reaction - typically made out of cadmium or boron.

3.2.1 Perform a first-hand investigation to observe radiation emitted from a nucleus using Wilson’s Cloud Chamber
Wilson’s Cloud Chamber: An early detector used in particle physics

The radiation ionises the vapour and creates a seed upon which vapour can condense.

• Alpha
• Heavy therefore they have low penetrating power
• Short track
• High charge therefore high ionising power
• Thick tracks
• Beta
• Relatively light therefore higher penetrating power
• Longer track
• Relatively lower charge therefore lower ionising power
• Thinner tracks as less vapour

3.2.2 Solve problems to calculate the mass defect and energy released in natural transmutation and fission reactions

Mass defect: Mass of atom - mass of nucleons
Binding Energy: = Mass defect * c2 (via Einstein’s E = MC2). If in amu look at data sheet.

4.1.1 Explain the basic principles of a fission reactor

Parts:

• Fuel Rods
• Where the fission takes place
• U-235 and Pu-239 ~ 4%
• Moderator
• Water/Graphite
• Slows down neutrons as slower neutrons are more likely to split uranium through collisions
• Thermal neutrons
• Coolant
• Water
• Prevent meltdown
• Control Rods
• Absorb neutrons to stop the reaction from going out of control
• Shielding
• Concrete

4.1.3 Describe how neutron scattering is used as a probe by referring to the properties of neutrons.

Neutron Scattering utilises the wave characteristics of neutrons to study the internal structure and properties of matter.

• Neutrons are extremely penetrative due to their neutral charge, and so can analyse the entire depth of a specimen unlike electron microscopes which only map the surface. Undeflected unless through collision.
• Neutrons can probe nuclei and have useful collisions because of their comparable size and mass to all nucleons.
• They can probe small or proton-rich materials, which make up organic matter, unlike electron microscopes, which fail due to the relatively low number of electrons.
• Magnetic moment of neutrons also allows for the study of magnetic properties.

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

Particle Accelerators collide high energy particles to:

• Probe the interior of nuclei and nucleons
• Produce new particles (convert energy released in a collision into mass through E = mc2)

This can further our knowledge of the subatomic (forces and composition) in order to predict new particles and make predictions about cosmological theories.

Cyclotron:

• Charged particles from the ion source ravel in semicircular arcs as they pass through the D
• Accelerated by high voltage as they pass from one D to another
• As velocity increases so does the radius
• At maximum velocity the particles are deflected towards a target.

Linear Accelerator:

• Charge particles are attracted to the first tube which is momentarily negative
• The charge accelerates in the electric field between the tubes and gains energy
• The oscillator’s frequency is arranged so that by the time the charge gets to the end of one tube the next tube has changed its polarity. The tube it is leaving repels it and it is attracted the the next tube which provides additional energy
• To compensate for the additional velocity each tube is made progressively longer than the previous one.

• They work in a similar way to cyclotrons, except that they keep the particles in a path of constant radius.
• As the particles gain energy, the magnetic field is increased to maintain the same path.
• The particles move through a small diameter evacuated tube that forms a large diameter ring.
• In certain regions throughout the ring, an applied radio frequency produces electric fields which to provide a “kick” to the particle to increase its energy.
• As the particles increase energy, the radio frequency increases accordingly as they travel through the cyclotron faster and faster.

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

Standard Model: Everything can be broken down into matter and forces

Fermions

• Matter Constituents
• Leptons
• Electron (-1)
• Electron Neutrino (0)
• Muon (-1)
• Muon Neutrino (0)
• Tau (-1)
• Tau Neutrino (0)
• Quarks
• Up (⅔)
• Down (-⅓)
• Strange (-⅓)
• Charm (⅔)
• Top (⅔)
• Bottom (-⅓)

Protons (2 up 1 down)

Neutrons (2 down 1 up)

Bosons

• Force Carriers
• Photons etc.

4.2.1 Analyse information to assess the significance of the Manhattan Project to Society

• Nuclear weaponry led to the early conclusion of WWII, sparing many lives and allowing nations to restabilise.
• Nuclear fission research led to the development of nuclear reactions allowing the development of nuclear power which reduced the consumption of fossil fuels. →  creating jobs at nuclear power plants.
• Production of radioisotopes for use in industry and medicine
• In medicine this has led to new methods in diagnostic imaging and treatment hence saving lives.
• In industry, radioisotopes allow precise measurements and imaging to be made.
• Countries are aware of the destroying power of nuclear weaponry and may avoid wars in the future.

• More than 100 000 people were killed in the bombing of Hiroshima and Nagasaki. There were thousands more deaths due to cancer caused by radiation in the following years.
• There are range of issues regarding nuclear wastes- which are difficult to dispose of and emit harmful radiation and the exposure of plant workers to radiation.
• There is also the danger of explosion occurring such as Chernobyl and Three Mile Island.
• Workers using radioisotopes are at a great danger of radiation exposure.
• The destructive potential of nuclear weapons have given men the ability to destroy ourselves.

4.1.2 Describe some medical and industrial applications of radioisotopes

and

4.2.2 Describe the use of isotopes in:

Medicine: Cobalt-60 a gamma emitter so it can kill cells in a tumor leading to a reduction in cancer. In addition it can sterilize surgical equipment to prevent infection.

Engineering: Cobalt-60 a gamma emitter which has high penetrating power and so can be used for thickness control and also for metal fatigue inspection when used with photo film.

Agriculture: Cobalt-60 is a gamma emitter and so can sterilize food to increase shelf life. Its long half life of 5.3 years means it doesn’t need replacement often and the same emitter can be used for multiple sterilisations.

Medicine: Tc-99m: Technetium-99m is a very commonly used radioisotope in medicine. This radioisotope has a short half-life of about six hours which minimises harm to the body. It decays from Te-99m to Te-99 by emitting a gamma ray, which can be detected by PET and other medical scanners. Te-99m is injected into patients’ bodies as a liquid solution where it will flow through the bloodstream, releasing gamma radiation as it does. This radiation gives a clear picture of the tissue structures inside the patient’s body.

Agriculture: P-32: a phosphate solution containing radioactive P-32 is injected into the root system of a plant. Chemically it behaves identically to P-31 that plants normally use in their biological processes, and its movement can be detected by a Geiger counter. By observing the movement of P-32 through the plant, scientists can determine the metabolic rate of plants and determine whether certain factors can affect this rate. E.g. this may be useful in researching the effect of certain fertilisers on certain crops. P-32 has a half life of 14 days and emits beta rays which means that it can be easily detected but disappears relatively quickly.
Engineering: Co-60: Cobalt-60 is used to detect stress fractures in metals, particularly in aircraft. Stress fractures occur when metals are repeatedly exposed to strong forces, such as those experienced by the wings of an aircraft. Small fractures can form which can eventually result in catastrophic failure. These fractures are extremely hard to detect, because they can occur inside a solid piece of metal, and are often extremely small. By placing cobalt-60 on one side of the metal, and a gamma detector on the other side (often photographic film), the cracks can be identified easily and non-destructively