Topic 7: Atomic and nuclear physics & AHL Topic 13 (SL option B): Quantum physics and nuclear physics

IB equations:

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Important Terms & Concepts:
• nucleus, proton, electron, neutron, photon, ion, neutrino
• isotope, nuclide, nucleon, atomic & mass number
• “plum pudding” model, Rutherford model, Bohr model, Schrodinger wave model
• black-body radiation, emission/absorption spectra, energy levels, Balmer lines, “electron in a box”
• photoelectric effect, de Broglie hypothesis, matter waves, Heisenberg uncertainty principle
• alpha, beta, gamma radiation, radioactivity, radioactive decay, half-life, decay constant,
• transmutation, fission, fusion, mass-energy equivalence, mass defect, binding energy, mass spectrometer
• Geiger – Marsden (Rutherford, Goldfoil) αlpha “Coulomb” scattering experiment
Important Experiments:
Milikan i) Oil Drop (mass & charge of e-) and ii) Photoelectric Effect experiment (proof for Einstein)
• Davisson–Germer experiment (electron as wave), electron diffraction experiments
HyperPhysics Atomic-Quantum
HyperPhysics Nuclear

7.1 The atom
Atomic Model - Tsokos: Atomic/Nuke Core Kirk Review: Atomic & Nuke I Course Companion Ch 16 Mech Universe Video - The Atom
• 7.1.1 Describe a model of the atom that features a small nucleus surrounded by electrons. (Students should be able to describe a simple model involving electrons kept in orbit around the nucleus as a result of the electrostatic attraction between the electrons and the nucleus.)

  • The model of the atom consists of a small central nucleus that is surrounded by electrons orbiting in circular orbits, organized in different energy levels.
  • The central nucleus contains most of the mass of the atom, where as the electrons provide the little mass of the negative charges.
  • The positive and negative charges attract each other by electrostatic attraction and are balance out to make the atom neutral.
- Sweta (Tim Kirk)external image -BCdUOrIkmcWjXRuoPshnNo2lUTCdrjK8vURonNtQDmK5fiGU1KXs_UHiPMQ19RFDu1bFbYKyVaK6vw8Ic5JrQV8zeLFu5PJFDyWvwFyDK6SCQHL_v4

• 7.1.2 Outline the evidence that supports a nuclear model of the atom. (A qualitative description of the Geiger Marsden experiment and an interpretation of the results are all that is required.)

  • Geiger Marsden/ Rutherford/ Gold-Foil Experiment
    • Positive alpha particles are “fired” through screens at a thin gold leaf
    • According to the mass and velocity of the alpha particles, it was predicted that the alpha particles would pass through the gold leaf.
    • They discovered that some of the alpha particle had deflected through huge angles. The deflection was caused by the alpha particle repelling off the nucleus.
    • - Sweta (Tim Kirk)
  • external image RWvCY5gyc16rhO3Wj4iePhXHlf7nxn_ZE5M4WPEMp90bIAyT55igYOluDb2-BXF6NNnnhUkmRW3DifkNY0vVNQc6VvnglVm840RjdhthZ0U8SKwfe-k

Thompson’s model compared to Rutherford’s modelexternal image 6TJxR_BUs05cRCBHY08Y5zPPyKO-nyVo_3MvLj7Kty9acXJHZbO59TlMHSzIz_RKPY1as-L1O-Nqok1xKulTdjltNNkCHXZXLjq_2pfkwMNtyS0Ff64
- Sweta (Tim Kirk)

• 7.1.3 Outline one limitation of the simple model of the nuclear atom.

    • The problem with this theory was that accelerating charges are known to lose energy. If the orbiting electrons were to lose energy they would spiral into the nucleus. The Rutherford model cannot explain to us how atoms are stable. (Kevin - __Allan Riddick__)
    • Charges that are accelerating radiate energy since it’s constantly changing direction as it moves in a circular orbit. Therefore, the charges would lose energy and move towards the nucleus. In this case, atoms can’t exist, proving that there is a fallacy in the model. (Sweta- Tsokos)
    • The simple model of the nuclear atom is limited because accelerated charges are known to radiate energy so orbital electrons should constantly lose energy (this changing direction means the electrons are accelerating). (prakash - kirk)

• 7.1.4 Outline evidence for the existence of atomic energy levels. (Students should be familiar with emission and absorption spectra, but the details of atomic models are not required. Students should understand that light is not a continuous wave but is emitted as “packets” or “photons” of energy, each of energy hf.)

  • This is found in the emission and absorption spectra.
  • By analyzing the frequencies of light emitted from an element, it is possible to figure out what it is. (Kevin - Kirk)
    • A Continuous spectrum would mean that all frequencies of the electromagnetic spectrum are present - light from the sun contains all visible wavelengths of light. (Kevin - Kirk)
    • An emission spectrum is not continuous (see Sweta’s photo) but contain certain frequencies of light relative to the discrete energy levels present in the atom. Each possible combination of drops in energy level (e.g. all the ones dropping to the 2th energy level of the hydrogen atom are all part of the Blamer series) emit different wavelengths of light enabling us to deduce what element created that light. (Kevin - Kirk)
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  • The different distances between the lines of color indicate the distance between each energy level, and the type of color indicates the amount of energy that is released when an electron moves from a higher energy level to a lower energy level. (Ilkyu Pudong Physics)

Nuclear structure
• 7.1.5 Explain the terms nuclide, isotope and nucleon.

    • Nuclide is a particular species of atoms whose nucleus contains a specified number of protons and a specified number of neutrons (protons and neutrons that form a nucleus) (Wamiq, Kirk)
    • Isotopes are element nuclides with the same number of proton but different number of neutrons. (Wamiq, Kirk)
    • Isotopes: Atoms that have the same atomic number but have a different neutron matter. This is because the number of neutrons can vary in an element. (Sweta- Rinehart Holt)
    • Protons and neutrons collectively are called Nucleons (Wamiq, Kirk)

  • Example: 611C , 612 C , 613C, 614C Four isotopes of Carbon (Sweta- Rinehart Holt)

• 7.1.6 Define nucleon number A, proton number Z and neutron number N.

  • ZAX- example external image pTlqytBqO2psj4yqnmGyPI7fHbTKTh6mObHbAKzEVRg7u-rPbZYF4as0xlsXmGyBrkn8qOUtZlnfSqbEV5IkCYKjP6tIFJtLvBnjsl-F-CUkxC9xWI4
  • Nucleon number (A) - mass number, equal to number of nucleons (Wamiq, Kirk)
  • Proton number (Z) - atomic number, equal to number of protons in the nucleus (Wamiq, Kirk)
  • Neutron number (N) - Mass Number - Proton Number, equal to number of neutrons in the nucleus (Wamiq, Kirk)
  • To calculate the neutron number of an isotope is determined by the relationship A= Z + N (the mass number of an atom A = the mass of protons Z added to the number of neutrons N). (Sweta- Rinehart Holt)
  • Add the number of Protons and the number of Neutrons to get the Neucleon number (Yun Hwan)external image -11ei4JgaPToaAN6iXXefUq3zH-Q35oI4I7CzstXjRxvERBj1kYw1WkBQ1b9yZ1KCxZUTqq0JhaFIr8EDejJ1IziRXX_XtAKtvjiLKhqdVRk2dKr8VA

(Yun Hwan- __Allan Riddick__)

• 7.1.7 Describe the interactions in a nucleus. (Students need only know about the Coulomb interaction between protons and the strong, shortrange nuclear interaction between nucleons.)

  • According to our knowledge of electrostatics a nucleus should not be stable. Protons are positive charges so should repel each other. There must be another force in the nucleus that overcomes the electrostatic repulsion and hold the nucleus together. This force is called the strong nuclear force. (Yun Hwan- __Allan Riddick__)
  • Strong nuclear forces must be very strong to overcome the electrostatic forces. They must also have a very small range as they are not observed outside of the nucleus. (Yun Hwan- __Allan Riddick__)
  • Neutrons have some involvement in strong nuclear forces. Small nuclei have equal numbers of protons and neutrons. Larger nuclei, which are harder to hold together, have a greater ratio of neutrons to protons. (Yun Hwan, Prakash- __Allan Riddick__)
  • The nucleons are held within the nucleus of the atom by a force called the strong nuclear force. This attractive force is stronger than the electrical force if the distance between the nucleons is small (r= 10-15m or less). Those with a greater distance are said to have a negligible nuclear force. (Sweta- Tsokos)
  • Nucleus consists of protons (positively charged) and neutrons (neutral). Together they are called nucleons. (Ilkyu - Pudong Physics)
  • Protons tend to repel against each other because of their positive electric force. (Ilkyu - Pudong Physics)
  • Strong nuclear force is another force that eists among the nucleons and that is what unites all the protons and neutrons together. (Ilkyu - Pudong Physics)
  • Strong nuclear force is greater than the electric force of protons which is why it is able to stabilize protons despite their repulsive forces. (Ilkyu - Pudong Physics)
  • Strong nuclear force is short-ranged, which is very strong when the distance between nucleons is less than 10^-15m apart. Beyond that distance, the force becomes zero. (Ilkyu - Pudong Physics)
  • Gravitational and electric forces on nucleus are long-ranged, which pushes away the approaching nucleons. (Ilkyu - Pudong Physics)
  • In order for strong nucleus force to apply to each other, they must be traveling at a higher speed (hot temperature) or be pushed against each other by a great force. (Ilkyu - Pudong Physics)

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  • According to our knowledge of electrostatics a nucleus should not be stable. Protons are positive charges so should repel each other. There must be another force in the nucleus that overcomes the electrostatic repulsion and hold the nucleus together. This force is called the strong nuclear force.
  • Strong nuclear forces must be very strong to overcome the electrostatic forces. They must also have a very small range as they are not observed outside of the nucleus.
  • Neutrons have some involvement in strong nuclear forces. Small nuclei have equal numbers of protons and neutrons. Larger nuclei, which are harder to hold together, have a greater ratio of neutrons to protons.

7.2 Radioactive decay
Radioactivity - Tsokos: Radioactivity/ Core Tsokos: Nuclear Reactions/ Core
• 7.2.1 Describe the phenomenon of natural radioactive decay. (The inclusion of the antineutrino in β− decay is required.)
• 7.2.2 Describe the properties of alpha (α)and beta (β) particles and gamma (γ) radiation.
• 7.2.3 Describe the ionizing properties of alpha (α) and beta (β) particles and gamma (γ) radiation.
• 7.2.4 Outline the biological effects of ionizing radiation. (Students should be familiar with the direct and indirect effects of radiation on structures within cells. A simple account of shortterm and longterm effects of radiation on the body is required.)
• 7.2.5 Explain why some nuclei are stable while others are unstable. (An explanation in terms of relative numbers of protons and neutrons and the forces involved is all that is required.)

• 7.2.6 State that radioactive decay is a random and spontaneous process and that the rate of decay decreases exponentially with time. (Exponential decay need not be treated analytically. It is sufficient to know that any quantity that reduces to half its initial value in a constant time decays exponentially. The nature of the decay is independent of the initial amount.)
• 7.2.7 Define the term radioactive halflife.
• 7.2.8 Determine the half-life of a nuclide from a decay curve.
• 7.2.9 Solve radioactive decay problems involving integral numbers of half-lives.

7.3 Nuclear reactions, fission and fusion
Nuclear reactions - Tsokos: Matter & Energy
• 7.3.1 Describe and give an example of an artificial (induced) transmutation.
• 7.3.2 Construct and complete nuclear equations.
• 7.3.3 Define the term unified atomic mass unit. (Students must be familiar with the units MeV c-2 and GeV c-2 for mass.)
• 7.3.4 Apply the Einstein mass–energy equivalence relationship.
• 7.3.5 Define the concepts of mass defect, binding energy and binding energy per nucleon.
• 7.3.6 Draw and annotate a graph showing the variation with nucleon number of the binding energy per nucleon. (Students should be familiar with binding energies plotted as positive quantities.)
• 7.3.7 Solve problems involving mass defect and binding energy.

Fission and fusion
• 7.3.8 Describe the processes of nuclear fission and nuclear fusion.
• 7.3.9 Apply the graph in 7.3.6 to account for the energy release in the processes of fission and fusion.
• 7.3.10 State that nuclear fusion is the main source of the Sun’s energy.
• 7.3.11 Solve problems involving fission and fusion reactions.

13.1 Quantum physics
The quantum nature of radiation - Tsokos: Quantum & Uncertainty Kirk Review: Quantum & Nuke II Course Companion Ch 17
• 13.1.1 Describe the photoelectric effect.

Under certain conditions, when light is shone onto a metal surface (such as zinc) electrons are emitted from the surface. This is the p.e effect. sanchit
  • Below a certain threshold frequency, no photo-electrons are emitted. sanchit
  • Above the threshold frequency, the maximum kinetic energy depends on the frequency of incident light.sanchit
  • The number of electrons emitted is directly related to intensity, the more intensity means the more number of electrons there are. sanchit
  • There is no noticeable delay between the arrival of the light and the emission of electrons. (Kevin - Kirk)

• 13.1.2 Describe the concept of the photon, and use it to explain the photoelectric effect. (Students should be able to explain why the wave model of light is unable to account for the photoelectric effect, and be able to describe and explain the Einstein model.)

  • Einstein introduced a new idea of thinking of light as being made up of particles, called photons. The energy photons carried by a photon is equal to E=hf. The wave model of light does not explain the photoelectric effect, since according to the wave model radiation of any frequency would eventually bring enough energy to the metal plate to free some electrons. This, however, is not true. The absorption of light by electrons is not continuous, but discrete. There is no continuous build up of energy, but energy is received in packets (photons). (Tom - Kirk Study Guide)
  • It is not enough to explain the photoelectric effect based on the classical theories: the kinetic energy to emit electrons depends on the intensity of light. Einstein extended the plank’s concept of quantization and integrated it to electromagnetic waves by introducing photons (stream of particles). Each photon carries energy (E=hf) packets of light that are discrete. (Sweta - Rinehart Holt)

• 13.1.3 Describe and explain an experiment to test the Einstein model. (Millikan’s experiment involving the application of a stopping potential would be suitable.)

  • The distance of closest approach of a particle to the nucleus can be found by using the law of conservation of energy. The initial energy of the particle is defined by Ek =12mv2 and then converted into potential energy as the charge approaches the nucleus (W = qαV). When this is equated with the kinetic energy, all the terms are known except the distance, which can therefore be found. (Kevin - WikiBooks)
  • Electrons at the surface need a certain minimum energy in order to escape from the surface. This minimum energy is called work function of the metal and has the symbol ϕ (Kevin - Kirk)
  • The Stopping Potential Experiment is what tests the electron model, the apparatus consists of a vacuum with opposing metal plates ( cathode and anode) where UV shines on the cathode and the photoelectric effect releases electrons in packets (discrete chunks, as opposed to continuous) called photoelectrons. They are accelerated across to the anode, through vacuum due to a potential difference created. This is going against the current, and the amount of voltage is steadily
  • The energy carried by a photon is given by
    • E = hf; E- energy in joules, h- Planck’s constant: 6.626068 × 10-34 m2 kg/s (Yun Hwan- Kirk)
  • The UV light energy arrives in lots of photons (prakash, kirk)
  • The energy in each packet is fixed by the frequency of UV light that is being used, whereas the number of packets arriving per second is fixed by the intensity of the source. (prakash, kirk)
  • Dirrferent electrons absorb different photons. If the energy of the photons. If the enerdy of the photon is large enough, it gives the electron enough energy to leave the surface of the metal. (prakash, kirk)
  • Extra energy would be retained by the electron as kinetic energy. (prakash, kirk)
  • The threshold frequency: incoming energy of photons = energy needed to leave the surface + kinetic energy; Thus a graph of frequency against stopping potential should be a straight line of gradient e/h.(prakash, kirk)

• 13.1.4 Solve problems involving the photoelectric effect.

  • Example: What is the maximum velocity of electrons emitted from a zinc surface (ϕ=4.2eV) when illuminated by EM radiation of wavelength 200nm? (Kevin - Kirk)
    • Capture.PNGCapture.PNG

The wave nature of matter Mech Universe Video - Particles & Waves
• 13.1.5 Describe the de Broglie hypothesis and the concept of matter waves. (Students should also be aware of wave–particle duality (the dual nature of both radiation and matter).)

The de Brogie hypothesis is that all moving particles have a “matter wave” associated with them. In other words, all moving particles exhibit a wave like nature. Both particles and radiation have a dual wave-particle nature. The de Broglie wavelength of a particle can be calculated using the following equation: =h/p=h/mv. (Tom - Kirk Study Guide)

This matter wave can be thought of as a probability function associated with the moving particle. The (amplitude)^2 of the wave at any given point is a measure of the probability of finding the particle at that point. (Prakash, kirk)

• 13.1.6 Outline an experiment to verify the de Broglie hypothesis. (A brief outline of the Davisson–Germer experiment will suffice.)

  • Davisson-Germer experiment: a beam of electron strikes a target nickel crystal. The electrons are scattered from the surface. The intensity of these scattered electrons depends on the speed of the electron and the angle. A maximum scattered intensity was recorded at an angle that quantitatively agrees with the constructive interference condition from adjacent atoms on the surface. Interference of these electrons shows that they have a wave-like nature. (Tom - Kirk Study Guide)
  • Electron diffraction experiment
    • electron wave travels through a gap of same order as its wavelength
      • crystals (such as powdered graphite) provides such spacing
    • when a beam of electrons goes through the powdered graphite, the electrons will be diffracted according to the wavelength
    • the diffraction is in the form of circles that correspond to the angles where constructive interference takes place(Erfan, Kirk)

• 13.1.7 Solve problems involving matter waves. (For example, students should be able to calculate the wavelength of electrons after acceleration through a given potential difference.)

Atomic spectra and atomic energy states Mech Universe Video - The Atom
• 13.1.8 Outline a laboratory procedure for producing and observing atomic spectra. (Students should be able to outline procedures for both emission and absorption spectra. Details of the spectrometer are not required.)

  • Emission spectra
    • Particular frequencies of light are produced when an element is hot enough to radiate light
    • This light needs to be split into its component frequencies using spectrometer (either a prism to defract the light or a diffraction grating) this creates a line spectrum
    • different frequencies are diffracted at different angles
    • the angle is used to calculate wavelengths and frequencies
    • (Erfan, New IB Course Companion)
  • Absorption Spectra

• 13.1.9 Explain how atomic spectra provide evidence for the quantization of energy in atoms. (An explanation in terms of energy differences between allowed electron energy states is sufficient.)

  • When an electron moves between energy levels it must emit or absorb energy. The energy emitted or absorbed corresponds to the difference between the two allowed energy levels. The energy is emitted or absorbed as photons. The lines in the atomic spectra correspond with the energy levels. (prakash, kirk)

• 13.1.10 Calculate wavelengths of spectral lines from energy level differences and vice versa.

E=hf=hc/ (Tom)
• 13.1.11 Explain the origin of atomic energy levels in terms of the “electron in a box” model. (The model assumes that, if an electron is confined to move in one dimension by a box, the de Broglie waves associated with the electron will be standing waves of wavelength 2L/n where L is the length of the box and n is a positive integer. Students should be able to show that the kinetic energy EK of the electron in the box is (n2h2)/(8meL2).)

  • The wavelike nature of electrons is hard to imagine in three dimensions, to simplify the situation we consider only one dimension in the electron in a box model
  • Different energy levels are predicted for the electron which correspond to the different possible standing waves
  • Ek=n2h28meL2 (Erfan, Kirk)

•13.1.12 Outline the Schrodinger model of the hydrogen atom. (The model assumes that electrons in the atom may be described by wave-functions. The electron has an undefined position, but the square of the amplitude of the wave-function gives the probability of finding the electron at a particular point.)

  • Copenhagen interpretation is a way to give a physical meaning to the mathematics of wave mechanics. (Wamiq, Kirk)
    • The description of particles is in terms of a wave function
    • At any instant of time, the wave function has different values at different points in space.
    • The mathematics of how this wave function develops is like the mathematics of a travelling wave.
    • The probability of finding the particle at any point in space within the atom is square of the amplitude of the wave function at that point.
    • Electron Wave Functions don’t have a fixed wavelength. As an electron move aways from the nucleus, it must lose kinectic energy because they have opposite charges.
  • The Schrödinger theory assumes as a basic principle that there is a wave associated to the electron and that wave is called the wavefunction. Schrödinger suggested that (x,t)2can be used to find the probability that an electron will be found near position(x,t). (Wamiq, Tokos)

• 13.1.13 Outline the Heisenberg uncertainty principle with regard to position–momentum and time–energy. (Students should be aware that the conjugate quantities, position–momentum and time–energy, cannot be known precisely at the same time. They should know of the link between the uncertainty principle and the de Broglie hypothesis. For example, students should know that, if a particle has a uniquely defined de Broglie wavelength, then its momentum is known precisely but all knowledge of its position is lost.)

The Heisenberg uncertainty principle identifies a fundamental limit to the possibly accuracy of any physical measurement. Conjugate properties, position-momentum and energy-time, cannot be known precisely at the same time.
where x is the uncertainty in the measurement of position
where p is the uncertainty in the measurement of momentum
where E is the uncertainty in the measurement of energy
where t is the uncertainty in the measurement of time
(Tom - Kirk Study Guide)

13.2 Nuclear physics - Tsokos: Nuclear Physics
• 13.2.1 Explain how the radii of nuclei may be estimated from charged particle scattering experiments. (Use of energy conservation for determining closest-approach distances for Coulomb scattering experiments is sufficient.)
• 13.2.2 Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer. (Students should be able to draw a schematic diagram of the Bainbridge mass spectrometer, but the experimental details are not required. Students should appreciate that nuclear mass values provide evidence for the existence of isotopes.)
• 13.2.3 Describe one piece of evidence for the existence of nuclear energy levels. (For example, alpha (α) particles produced by the decay of a nucleus have discrete energies; gammaray (γ-ray) spectra are discrete. Students should appreciate that the nucleus, like the atom, is a quantum system and, as such, has discrete energy levels.)

Radioactive decay
• 13.2.4 Describe β+ decay, including the existence of the neutrino. (Students should know that β energy spectra are continuous, and that the neutrino was postulated to account for these spectra.)
• 13.2.5 State the radioactive decay law as an exponential function and define the decay constant. (Students should know that the decay constant is defined as the probability of decay of a nucleus per unit time.)
• 13.2.6 Derive the relationship between decay constant and half-life.
• 13.2.7 Outline methods for measuring the half-life of an isotope. (Students should know the principles of measurement for both long and short halflives.)
• 13.2.8 Solve problems involving radioactive half-life.