17 PROBING DEEP INTO MATTER Creation and Annihilation Describe differences between matter and antimatter Apply conservation laws to annihilation and materialisation events Explain how antimatter is used in medical imaging (PET) Starter: Can you give reasons why imaging the brain using x rays may have limitations or drawbacks.

Conventional x ray imaging does not show soft tissue well Conventional x ray imaging is a “2 dimensional” technique Computerised axial tomography can give 3D information but x ray dose is higher than conventional x ray imaging X ray techniques cannot map brain activity, only show structures

Read pages 189-191 Answer the following: What does PET stand for? Try and summarise in you own words how it works. 3) What is the main difference between matter and antimatter? What is the one thing that is the same? Ext: 4) What is meant by creation, annihilation and pair production?

Energy, momentum and Electric Charge conserved

Annihilation and Creation

Pair Production

Starter… An electron and a positron with negligible kinetic energy annihilate and produce two identical gamma ray photons. (Rest mass of electron =9.11x10-31kg, h=6.63x10-34Js, c = 3x108 ms-1) Calculate a) the energy released (in J and MeV) b) the frequency of the gamma-photons (in Hz).

Particle interactions Describe how charged particles interact via virtual photon exchange Explain how to describe these processes using Feynman diagrams and the “try all paths” approach Discuss consequences of the differences between fermions and bosons Starter: What are the maximum and minimum amplitudes that can result from adding two phasors, each of length 1 unit, and what are the phase differences in each case?

Starter: Explain the point this diagram is making…. “Try all paths” is a quantum rule obeyed by all photons and electrons. The same idea is applied to interactions of particles. Richard Feynman invented a type of diagram to help physicists keep track of all the possible ways that particles can interact. The rule “try all paths” changes to “try everything allowed” or more technically “everything that is not forbidden is compulsory”. Source Detector

To find out.......... What is a fermion? Give an example of a particle that is a fermion. What happens if you try to squeeze two fermions into the same region of space? Can you describe one important consequence of this? What is a boson? Give an example of a particle that is a boson. What happens if two identical bosons encounter each other? Can you give one important practical application of this?

Electron spin Photon spin

Fermions and Bosons Fermions ½ integer spin (1/2, 3/2,....) Electrons, Protons etc. Never occupy same quantum state (Avoid each other always) Consequently..... Two electrons in same orbital of an atom must have opposite spin (Pauli exclusion principle) Matter is “hard”: atoms are difficult to squash! Bosons Integer spin (0,1,...) Photons Can occupy same quantum state (Can “flock” together in step) Consequently..... In a laser, lots of photons join together to produce beam of photons all of identical phase and polarisation

Fermions and Bosons Fermions ½ integer spin (1/2, 3/2,....) Electrons, Protons etc. Never occupy same quantum state (Avoid each other always) Consequently..... Two electrons in same orbital of an atom must have opposite spin (Pauli exclusion principle) Matter is “hard”: atoms are difficult to squash! Bosons Integer spin (0,1,...) Photons Can occupy same quantum state (Can “flock” together in step) Consequently..... In a laser, lots of photons join together to produce beam of photons all of identical phase and polarisation

Light Amplification by Stimulated Emission of Radiation

Starter For each of the following statements, say whether it applies to FERMIONS or BOSONS: Q1. A photon is an example of this class of particle. Q2. These particles have integer spin values. Q3. Particles which cannot occupy the same quantum state. Q4. “Matter” particles, like protons, neutrons and electrons belong to this class. Q5. Virtual particles which are exchanged between interacting matter particles belong to this class. Q6. These particles can have spin values of 1/2, 3/2, 5/2 etc. Q7. (For chemistry students): Two electrons cannot occupy the same quantum state. How is it then possible to get two electrons into the same orbital? Hint: in what way are the two electrons distinguishable when in the same orbital?

Conservation in nuclear processes Explain why a new particle was needed to account for the energy spectrum of beta particles Balance nuclear equations: charge, mass-energy, baryon number, lepton number

The Baryon Family Baryons contain three quarks (we come to them later). Protons and neutrons are baryons! Baryon number must be conserved. Baryon number is +1 for all protons and -1 for anti-protons. Note: Protons and neutrons are also described as nucleons.

Leptons – fundamental particles Leptons are fundamental particles. As far as we are aware they are not made up of anything smaller. Examples are electrons and neutrinos. Leptons are given a property called lepton number. Electrons and neutrinos are given lepton number 1. Where as the antiparticles are given lepton number -1. All hadrons (non-leptons, which we learn more about later) have lepton number 0.

Rutherford’s experiment Describe how alpha scattering changed our view of atomic structure Explore effects of changing alpha particle energy and nuclear charge on scattering Estimate upper limit on nuclear size

Starter: Q1. I have a charge of +1 and a lepton number of -1. What could I be? Q2. I have a charge of zero and a lepton number of +1. What could I be? Q3. I have a baryon number of +1, a lepton number of zero and a charge of +1. What could I be? Q4. I have a baryon number of +1 and a charge of zero. What Q5. I have a baryon number of -1 and a charge of -1. What could I be?

Starter: Q1. I have a charge of +1 and a lepton number of -1. What could I be? ANTIELECTRON (POSITRON) Q2. I have a charge of zero and a lepton number of +1. What could I be? NEUTRINO Q3. I have a baryon number of +1, a lepton number of zero and a charge of +1. What could I be? PROTON Q4. I have a baryon number of +1 and a charge of zero. What could I be? NEUTRON Q5. I have a baryon number of -1 and a charge of -1. What could I be? ANTIPROTON

Gravitational and electric fields compared Q1. (a) Write down the expression for the force F between two masses, M and m, separated by a distance R. Q1. (b) Write down the corresponding expression for the force F between two charges Q and q, separated by a distance R. (The constant in the equation is known as the electric force constant, and is denoted by k.) Q2. (a) Write down the expression for the gravitational potential energy for an object of mass m at a distance R from the centre of a planet of mass M. Q2. (b) Write down the corresponding expression for the gravitational potential energy of a charge +q at a distance R from another charge +Q. Q3. (a) How much kinetic energy would you need to give the object in Q2. (a) for it to be able to “climb out” of the potential well of the planet? Q3. (b) How much kinetic energy would the charge +q in Q3. (a) have if it was released and allowed to coast far away from +Q?

Rutherford’s experiment Note: an alpha particle Is a helium nucleus with the electrons removed. So it is positively charged!

Rutherford’s observation Copy and complete the table using the statements provided Rutherford’s observation Explanation Model of the atom A. Most alpha particles passed straight through the foil, undeflected B. Some were deflected off course as they passed through C. Some bounced right back from the foil the nucleus is positively charged, while the electrons are outside it, far away nearly all the mass of the atom is in the nucleus there must be centres of + charge in the atom the nucleus is tiny compared to the overall size of the atom the atom is mostly empty space the centres of + charge must be much heavier than the alpha particles

Rutherford’s observation Explanation Model of the atom A. Most alpha particles passed straight through the foil, undeflected The atom is mostly empty space. The nucleus is tiny compared to the overall size of the atom B. Some were deflected off course as they passed through There must be centres of + charge in the atom. The nucleus is positively charged, while the electrons are outside it, far away C. Some bounced right back from the foil The centres of +charge must be much heavier than the alpha particles Nearly all of the mass of the atom is in the nucleus

Measuring the size of nuclei Explain how electron diffraction can be used to measure nuclear size accurately and precisely Determine nuclear diameter from scattering curves Describe and explain the relationship between nuclear size and nucleon number Starter: From your AS physics waves knowledge, explain the appearance of all features of the single-slit diffraction curve shown below:

JJ and GP Thomson: father and son Nobel physics prize winners Whatever, Dad. I got it for showing that the electron is a wave! Listen sonny, I got the Nobel prize for showing that the electron is a particle...

Wave-particle duality Evidence for wave-like character Evidence for particle-like character Light Electrons

Electron diffraction This eerie green glow is caused by low energy electrons in a cathode ray tube striking the phosphorescent coating on the inside of the glass bulb just behind the ruler.  In this case the diffraction is caused by the electrons passing through a thin layer of polycrystalline graphite (pencil "lead"). The regular array of carbon atoms in the crystals is responsible for the diffraction effects.

How does the electron energy affect what is seen in an electron diffraction experiment? Diffraction of low energy electrons Diffraction by planes of atoms of low energy electrons gives a diffraction pattern that reveals the inter atomic spacing. Here, the de Broglie wavelength of the electrons is quite large, as their momentum is small. The wavelength is comparable to the inter atomic spacing, so we get a lot of diffraction by the planes of atoms in the manner of a diffraction grating diffracting light. Diffraction of high energy electrons With very high energy electrons, the de Broglie wavelength is comparable to the size of a nucleus, and the diffraction effects seen are essentially the same as single slit diffraction. The atomic nucleus behaves as an obstacle for the electrons to diffract around, and the diffraction patterns seen is essentially the same as we get when light passes through a single slit.

Electron diffraction Q1. Explain why there is a minimum in the curve. Q2. What would be the effect on the curve of using higher energy electrons? Q3. What would be the effect on the curve of using a sample of argon-40 in place of neon-20?

Volume of nucleus is proportional to number of particles it contains. KEY POINT Volume of nucleus is proportional to number of particles it contains.

Nuclear density questions... Q1. If nuclear volume is proportional to the number of nucleons (A) in the nucleus, explain why nuclear radius r is given by: r = r0 A1/3 where r0 is a constant. Q2. The nucleon number of a gold nucleus is 197. The radius of the nucleon is 1.2x10-15m. Calculate the radius r of the gold nucleus. Calculate volume of the gold nucleus. The mass of a nucleon is 1.67x10-27kg, calculate the nuclear density. Q3. Silver has a mass number of 108. What is its nuclear density?

The structure of nucleons Explain why electrons are well suited to be a probe of nucleon structure Deduce the quark composition of a range of hadrons (baryons and mesons) Starter: Explain why alpha particles and protons are not well suited to probing the size of nuclei

Particle Family Tree All particles As we currently understand!! Fundamental particles (no internal structure) Leptons (electron, muon, tau, neutrinos) Exchange Particles Gluon, W, Z, photon Non-fundamental Particles Hadrons (made of quarks) Baryons (contains 3 quarks) e.g. Proton, neutron Mesons (quark + antiquark) e.g. Pion, kaon As we currently understand!!

Quarks The building blocks of protons and neutrons, and other fundamental particles. Two flavours of quark… The up quark (+ 2/3 e) and the down quark (– 1/3 e). The first direct evidence for quarks was obtained when very high-energy electrons (approx. 20Gev) in a beam were scattered from a stationary target as if there were point-like scattering centres in each proton or neutron. Quarks do not exist in isolation. They are bound together by the exchange of gluons (since they are the glue that hold the quarks together).

Colour charge Quarks have a new type of charge called colour charge. The charge comes in 3 types. Red, Green and Blue. They aren't actually coloured. Reason for colour charge is you need one of each colour to make a proton or neutron just like you need all colours to make white.

You cant really separate quarks!!!

WAVES PARTICLES Light Electrons Starter: Copy the table and fill in each box with example(s) of each phenomenon WAVES PARTICLES Light Electrons

Why are atoms mostly empty space? Chemistry questions that only physics can answer..... DISCUSS IN PAIRS Why are atoms mostly empty space? Why don’t the electrons just fall into the nucleus? Why are only some energy levels allowed for electrons in an atom or a molecule? Why does delocalisation of electrons stabilise a molecule? Why are carrots orange?

The classical atom dethroned Explain the flaws in the “solar system” model of the atom Investigate an electron-wave atomic model Use an electron-wave model to explain both the stability of aromatics and the origin of colour in chemistry

What is the problem?!? Maxwell’s theory which states that an electron being accelerated in an electric field will emit radiation. Hint: Think about the Diamond visit!

Wave-Particle Duality (for electrons) AS-RECAP Wave-Particle Duality (for electrons) What is the evidence?!? de Broglie λ = h/p = h/mv m=9.1x10-31kg h=6.6x10-34Js

Standing Waves… AS-RECAP Allowed discrete values of wavelengths only…. Ie L = n λ /2 L-length of string n – harmonic

Electrons in atoms… (QM) Atoms can be thought of as a box in which electrons are trapped. Results of model: Electrons can only occupy certain discrete energy levels in atoms. Each level has a different associated standing wave of a particular λ.

Putting de Broglie and standing waves together….

Beta carotene….. ….gives carrots and pumpkins their orange colour ….in humans, is converted into retinal, which is essential for the vision process A conjugated system with alternating single and double bonds Average carbon-carbon bond length = 140 pm (1 pm = 10-12 m) 2 delocalisable electrons per double bond Challenge Can you use the equation for electron delocalisation in one dimension (particle in a box) to : determine the pattern of energy levels in beta carotene, calculate the wavelength at which it absorbs light.

Beta-carotene: a chromophore modelled as a particle in a box A conjugated system with alternating single and double bonds Average carbon-carbon bond length = 140 pm Calculate the length over which electrons are delocalised Identify the quantum numbers of the highest-occupied and lowest unoccupied energy levels Use the formula E=n2h2/8mL2 to calculate the energies of these levels Calculate the energy and wavelength of the photon that would be absorbed if an electron was excited from the highest-occupied to lowest-unoccupied level

Why are atoms mostly empty space? Chemistry questions that only physics can answer..... Why are atoms mostly empty space? Why don’t the electrons just fall into the nucleus? Why are only some energy levels allowed for electrons in an atom or a molecule? EXPLAINED WITH BASIC MODEL Why does delocalisation of electrons stabilise a molecule? EXPLAINED WITH BASIC MODEL Why are carrots orange? EXPLAINED WITH BASIC MODEL

Starter In the last lesson, we modelled the electron in an atom by treating the electron as a standing wave confined to a potential well. Q1. Which of the following feature(s) of the atom did this model reproduce? Quantised electron energies (electrons can only have certain energies within the atom)? Energy levels becoming closer together with increasing energy, as is observed in the spectra of atoms? Q2. The model could be used to describe delocalised electrons in molecules such as benzene and carotene, and thereby explain why delocalisation (resonance) stabilises these molecules, and how colour arises in them. Using the energy level expression derived from the model, explain why allowing electrons to spread out in a molecule leads to stabilisation. Explain how to calculate the energy of a photon absorbed by a molecule with delocalised electrons.

Finally, a model for the atom that fits experimental data! Develop an electron-wave model that incorporates potential energy Use the model to investigate atom stability Calculate energy levels and atomic radii with the model, and see if they match experiment

Considering Potential energy properly…

Considering Potential energy properly… KEY POINT: If size is too small, the kinetic energy is too large for electrical potential to bind the electron.

The Bohr model of the atom Total Energy = Kinetic Energy + Potential Energy Q1. Which of the terms in the equation above is always positive, and which is always negative? Q2. For a stable atom, one where the electron is bound, to the nucleus, what must be true about the sum of KE+PE? Potential energy PE = -Zke2 / r where r is the nucleus-electron distance, e is the charge on the electron and k is a constant (=1/4πε0) What will happen to the PE if the electron is confined in a smaller space closer to the nucleus? Kinetic Energy KE = h2 / 2mλ2 where λ is the wavelength of the standing wave describing the electron What will happen to the KE if the electron is confined in a smaller space closer to the nucleus?

Why are atoms mostly empty space? Chemistry questions that only physics can answer..... Why are atoms mostly empty space? EXPLAINED WITH BOHR MODEL (electron wave + PE) Why don’t the electrons just fall into the nucleus? Why are only some energy levels allowed for electrons in an atom or a molecule? EXPLAINED CORRECTLY WITH BOHR MODEL (electron wave + PE) Why does delocalisation of electrons stabilise a molecule? EXPLAINED WITH BASIC MODEL (particle in a box) Why are carrots orange? EXPLAINED WITH BASIC MODEL (particle in a box)

Starter : Explaining atomic structure   Explain the following statements carefully, using the key words in italics provided if need be. An electron in orbit around a nucleus does not radiate energy and fall into the nucleus as predicted by classical physics. Matter is mostly empty space, with the atomic nucleus occupying a tiny fraction of the volume of the atom. The energy levels occupied by an electron in atom can have only certain values described by a quantum number n, where n = 1, 2, 3 etc. Atoms absorb and emit light only at certain specific wavelengths. wave-particle duality standing wave destructive interference de Broglie wavelength kinetic energy potential energy stability photon energy

Energy levels and spectra Use atomic energy level data to calculate emission and absorption spectra Interpret results of the Franck-Hertz experiment in terms of atomic energy levels

Energy levels in hydrogen En = -13.6/n2

Questions…. Q1. What is the wavelength of the Red and blue Balmer lines? Q2. If the wavelength of an emitted photon was 102 nm, which transition from the Lyman series caused it?

The Franck-Hertz experiment Sketch of Franck-Hertz Apparatus The Franck-Hertz experiment

The Franck-Hertz experiment Why does the current suddenly drop sharply? Why does the drop occur at different beam energies for different elements?

A hydrogen atom has energy levels at -13.6 eV (ground state, containing one electron), -3.4 eV, -1.5 eV, -0.9 eV. The energy levels are measured with respect to the ionisation limit, 0.0 eV. Calculate the wavelength of the lowest-energy photon that could be absorbed when an electron in the ground state of a hydrogen atom is excited to an upper energy level. [3] (Data: h = 6.6 x 10-34 Js, c = 3 x 108 ms-1, e = 1.6 x 10-19 C) (b) Electrons of energy 9 eV are fired through hydrogen gas in its ground state. The electrons are scattered without loss of energy. When the experiment is repeated with electrons of 11 eV energy, the electrons are scattered inelastically, emerging with energies of about 1 eV. Explain these observations. [3]