Essential idea: The microscopic quantum world offers a range of phenomena whose interpretation and explanation require new ideas and concepts not found in the classical world. Nature of science: (1) Observations: Much of the work towards a quantum theory of atoms was guided by the need to explain the observed patterns in atomic spectra. The first quantum model of matter is the Bohr model for hydrogen. (2) Paradigm shift: The acceptance of the wave–particle duality paradox for light and particles required scientists in many fields to view research from new perspectives. Understandings:
• Photons Blackbody spectrum
• The photoelectric effect Photoelectric effect
• Matter waves Wave interferenceDr. Quantum matter wavesQuantum-wave interferenceWhat does quantum interference look like?deBroglie-Bohm pilot waves vs. Copenhagen interpretation
• Pair production and pair annihilation
• Quantization of angular momentum in the Bohr model for hydrogen Models of the hydrogen atomThe hydrogen atom (for real)Discharge tubes
• The wave function Solving the Schrodinger equationAnother version of the same...The solutions and their pictures
• The uncertainty principle for energy and time and position and momentum
• Tunnelling, potential barrier and factors affecting tunnelling probability Applications and skills:
• Discussing the photoelectric effect experiment and explaining which fea-tures of the experiment cannot be explained by the classical wave theory of light
• Solving photoelectric problems both graphically and algebraically
• Discussing experimental evidence for matter waves, including an experi-ment in which the wave nature of electrons is evident
• Stating order of magnitude estimates from the uncertainty principle Guidance:
• The order of magnitude estimates from the uncertainty principle may include (but is not limited to) estimates of the energy of the ground state of an atom, the impossibility of an electron existing within a nucleus, and the lifetime of an electron in an excited energy state
• Tunnelling to be treated qualitatively using the idea of continuity of wave functions Data Booklet reference:
• E = hf . . . . . . . . . Energy of a quanta - Planck / Einstein
• Emax= hf - f . . . . . Photoelectric effect - Einstein
• E = - 13.6 / n2 eV . Energy of the hytrogen atom - Bohr
• mvr = nh / 2p . . . . Quantization of angular momentum - Bohr, de Broglie
• P(r) = | Y |2∆V . . . Wave function - Schrodinger
• ∆x∆p³h / 4p . . . . Heisenberg uncertainty principle
• ∆E∆t³h / 4p . . . . Heisenberg uncertainty principle
• The E represents the energy in a quantum of light (a photon) having a frequency f. The Planck constant h = 6.63x10-34 Js. The Emax represents the kinetic energy of a freed electron, and the f represents the work function, or the energy needed to free an electron from a photosensitive metal. The -13.6 / n2 represents the energy in eV of a hydrogen atom having its electron at the nth energy level. The m represents the mass of an electron, the v its velocity, and the r its "orbital" radius when located at the nth energy level of the hydrogen atom. The quantity mvr represents the angular momentum of the electron and the equation represents the quantization of the angular momentum due to the de Broglie hypothesis. The P(r) represents the probability of an electron represented with wave function Y being located at radius r if it has a potential ∆V. The ∆x represents the uncertainty in position of a particle having a momentum whose uncertainty is ∆p. The ∆E represents the uncertainty in energy of a particle having a time whose uncertainty is ∆t. Theory of knowledge:
• The duality of matter and tunnelling are cases where the laws of classical physics are violated. To what extent have advances in technology enabled paradigm shifts in science? Utilization:
• The electron microscope and the tunnelling electron microscope rely on the findings from studies in quantum physics
• Probability is treated in a mathematical sense in Mathematical studies SL sub-topics 3.6–3.7 Aims:
• Aim 1: study of quantum phenomena introduces students to an exciting new world that is not experienced at the macroscopic level. The study of tunneling is a novel phenomenon not observed in macroscopic physics.
• Aim 6: the photoelectric effect can be investigated using LEDs
• Aim 9: the Bohr model is very successful with hydrogen but not of any use for other elements

Essential idea: The idea of discreteness that we met in the atomic world continues to exist in the nuclear world as well. Nature of science: (1) Theoretical advances and inspiration: Progress in atomic, nuclear and particle physics often came from theoretical advances and strokes of inspiration. (2) Advances in instrumentation: New ways of detecting subatomic particles due to advances in electronic technology were also crucial. (3) Modern computing power: (4) Finally, the analysis of the data gathered in modern particle detectors in particle accelerator experiments would be impossible without modern computing power. Understandings:
• Rutherford scattering and nuclear radius Rutherford's Geiger-Marsden scattering experimentRutherford scattering simulation
• Nuclear energy levels
• The neutrino Balancing nuclear equations
• The law of radioactive decay and the decay constant Alpha decayBeta decay Applications and skills:
• Describing a scattering experiment including location of minimum intensity for the diffracted particles based on their de Broglie wavelength
• Explaining deviations from Rutherford scattering in high energy experiments
• Describing experimental evidence for nuclear energy levels
• Solving problems involving the radioactive decay law for arbitrary time intervals
• Explaining the methods for measuring short and long half-lives Guidance:
• Students should be aware that nuclear densities are approximately the same for all nuclei and that the only macroscopic objects with the same density as nuclei are neutron stars
• The small angle approximation is usually not appropriate to use to deter-mine the location of the minimum intensity Data Booklet reference:
• R = R0A1/3
• N = N0e - (lambda) t
• A = lN0e - (lambda) t
• sinq = l / d
• The radius of a nucleus is represented by R. The Fermi radiusR0 = 1.20x10-15 m. The atomic number is represented by A. The N represents the number of a sample of radioactive nuclei that remain. The N0 represents the initial population of a radioactive sample. The lambda l represents the decay constant of a radioactive nuclide. The t represents the time over which the decay occurs. The A represents the activity of a sample. Theory of knowledge:
• Much of the knowledge about subatomic particles is based on the models one uses to interpret the data from experiments. How can we be sure that we are discovering an “independent truth” not influenced by our models? Is there such a thing as a single truth? Utilization:
• Knowledge of radioactivity, radioactive substances and the radioactive decay law are crucial in modern nuclear medicine (see Physics option sub-topic C.4) Aims:
• Aim 2: detection of the neutrino demonstrates the continuing growing body of knowledge scientists are gathering in this area of study

TOPIC 12 PROBLEM SET

This is the complete problem set for Topic 12 - the same one I hand out. If you lose yours, you can download this one to replace it.

These are the Formative Assessments (practice) that you will do in order to prepare yourself for the Summative Assessments (evidence of proficiency). You can expect to receive a mark of at least Proficient on the Summative Assessment if you understand everything on these Formative Assessments.

Project marks are meant to replace summative assessment marks. Projects are your last opportunity to demonstrate your proficiency in meeting the standards of the assessment criteria.

## Quantum and nuclear physics

## 16 hours

## 12.1 – The interaction of matter with radiation

Essential idea:The microscopic quantum world offers a range of phenomena whose interpretation and explanation require new ideas and concepts not found in the classical world.Nature of science:(1) Observations: Much of the work towards a quantum theory of atoms was guided by the need to explain the observed patterns in atomic spectra. The first quantum model of matter is the Bohr model for hydrogen. (2) Paradigm shift: The acceptance of the wave–particle duality paradox for light and particles required scientists in many fields to view research from new perspectives.Understandings:• Photons Blackbody spectrum

• The photoelectric effect Photoelectric effect

• Matter waves Wave interference Dr. Quantum matter waves Quantum-wave interference What does quantum interference look like? deBroglie-Bohm pilot waves vs. Copenhagen interpretation

• Pair production and pair annihilation

• Quantization of angular momentum in the Bohr model for hydrogen Models of the hydrogen atom The hydrogen atom (for real) Discharge tubes

• The wave function Solving the Schrodinger equation Another version of the same... The solutions and their pictures

• The uncertainty principle for energy and time and position and momentum

• Tunnelling, potential barrier and factors affecting tunnelling probability

Applications and skills:• Discussing the photoelectric effect experiment and explaining which fea-tures of the experiment cannot be explained by the classical wave theory of light

• Solving photoelectric problems both graphically and algebraically

• Discussing experimental evidence for matter waves, including an experi-ment in which the wave nature of electrons is evident

• Stating order of magnitude estimates from the uncertainty principle

Guidance:• The order of magnitude estimates from the uncertainty principle may include (but is not limited to) estimates of the energy of the ground state of an atom, the impossibility of an electron existing within a nucleus, and the lifetime of an electron in an excited energy state

• Tunnelling to be treated qualitatively using the idea of continuity of wave functions

Data Booklet reference:•

E=hf. . . . . . . . . Energy of a quanta - Planck / Einstein•

Emax=hf-f. . . . . Photoelectric effect - Einstein•

E= - 13.6/ n2 eV . Energy of the hytrogen atom - Bohr•

mvr=nh/ 2p . . . . Quantization of angular momentum - Bohr, de Broglie•

P(r) = | Y |2∆V. . . Wave function - Schrodinger• ∆

x∆p³h/ 4p . . . . Heisenberg uncertainty principle• ∆

E∆t³h/ 4p . . . . Heisenberg uncertainty principle• The

Erepresents the energy in a quantum of light (a photon) having a frequencyf. The Planck constanth= 6.63x10-34 Js. TheEmax represents the kinetic energy of a freed electron, and thefrepresents the work function, or the energy needed to free an electron from a photosensitive metal. The -13.6/ n2 represents the energy in eV of a hydrogen atom having its electron at thenth energy level. Themrepresents the mass of an electron, thevits velocity, and therits "orbital" radius when located at thenth energy level of the hydrogen atom. The quantitymvrrepresents the angular momentum of the electron and the equation represents the quantization of the angular momentum due to the de Broglie hypothesis. TheP(r) represents the probability of an electron represented with wave function Y being located at radiusrif it has a potential ∆V. The ∆xrepresents the uncertainty in position of a particle having a momentum whose uncertainty is ∆p. The ∆Erepresents the uncertainty in energy of a particle having a time whose uncertainty is ∆t.Theory of knowledge:• The duality of matter and tunnelling are cases where the laws of classical physics are violated. To what extent have advances in technology enabled paradigm shifts in science?

Utilization:• The electron microscope and the tunnelling electron microscope rely on the findings from studies in quantum physics

• Probability is treated in a mathematical sense in

Mathematical studies SLsub-topics3.6–3.7Aims:•

Aim 1:study of quantum phenomena introduces students to an exciting new world that is not experienced at the macroscopic level. The study of tunneling is a novel phenomenon not observed in macroscopic physics.•

Aim 6:the photoelectric effect can be investigated using LEDs•

Aim 9:the Bohr model is very successful with hydrogen but not of any use for other elements## 12.2 – Nuclear physics

Essential idea:The idea of discreteness that we met in the atomic world continues to exist in the nuclear world as well.Nature of science:(1) Theoretical advances and inspiration: Progress in atomic, nuclear and particle physics often came from theoretical advances and strokes of inspiration. (2) Advances in instrumentation: New ways of detecting subatomic particles due to advances in electronic technology were also crucial. (3) Modern computing power: (4) Finally, the analysis of the data gathered in modern particle detectors in particle accelerator experiments would be impossible without modern computing power.Understandings:• Rutherford scattering and nuclear radius Rutherford's Geiger-Marsden scattering experiment Rutherford scattering simulation

• Nuclear energy levels

• The neutrino Balancing nuclear equations

• The law of radioactive decay and the decay constant Alpha decay Beta decay

Applications and skills:• Describing a scattering experiment including location of minimum intensity for the diffracted particles based on their de Broglie wavelength

• Explaining deviations from Rutherford scattering in high energy experiments

• Describing experimental evidence for nuclear energy levels

• Solving problems involving the radioactive decay law for arbitrary time intervals

• Explaining the methods for measuring short and long half-lives

Guidance:• Students should be aware that nuclear densities are approximately the same for all nuclei and that the only macroscopic objects with the same density as nuclei are neutron stars

• The small angle approximation is usually not appropriate to use to deter-mine the location of the minimum intensity

Data Booklet reference:•

R=R0A1/3•

N=N0e - (lambda)t•

A= lN0e - (lambda)t• sin

q= l/ d• The radius of a nucleus is represented by

R. TheFermi radiusR0 = 1.20x10-15 m. The atomic number is represented byA. TheNrepresents the number of a sample of radioactive nuclei that remain. TheN0 represents the initial population of a radioactive sample. The lambda l represents thedecay constantof a radioactive nuclide. Thetrepresents the time over which the decay occurs. TheArepresents the activity of a sample.Theory of knowledge:• Much of the knowledge about subatomic particles is based on the models one uses to interpret the data from experiments. How can we be sure that we are discovering an “independent truth” not influenced by our models? Is there such a thing as a single truth?

Utilization:• Knowledge of radioactivity, radioactive substances and the radioactive decay law are crucial in modern nuclear medicine (see

Physicsoption sub-topicC.4)Aims:•

Aim 2:detection of the neutrino demonstrates the continuing growing body of knowledge scientists are gathering in this area of study## TOPIC 12 PROBLEM SET

This is the complete problem set for Topic 12 - the same one I hand out. If you lose yours, you can download this one to replace it.## TOPIC 12 FORMATIVE ASSESSMENTS

These are the Formative Assessments (practice) that you will do in order to prepare yourself for the Summative Assessments (evidence of proficiency). You can expect to receive a mark of at least Proficient on the Summative Assessment if you understand everything on these Formative Assessments.## TOPIC 12 PROJECTS

Project marks are meant to replace summative assessment marks. Projects are your last opportunity to demonstrate your proficiency in meeting the standards of the assessment criteria.## EXTENSION NOTES FOR ENRICHMENT