Modern Physics

Learning Objective 15.1.A: Describe the properties and behavior of an object that exhibits both particle-like and wave-like behavior.

• 15.1.A.1 Quantum theory was developed to explain observations of matter and energy that could not be explained using classical mechanics. These phenomena include, but are not limited to, atomic spectra, blackbody radiation, and the photoelectric effect.
  • 15.1.A.1.i Quantum theory is necessary to describe the properties of matter at atomic and subatomic scales.
  • 15.1.A.1.ii In quantum theory, fundamental particles can exhibit both particle-like and wave-like behavior.
• 15.1.A.2 Light can be modeled both as a wave and as discrete particles, called photons.
  • 15.1.A.2.i A photon is a massless, electrically neutral particle with energy proportional to the photon's frequency.
    • Relevant equations:
    • $E = hf$
    • $\lambda = \dfrac{c}{f}$
  • 15.1.A.2.ii Photons travel in straight lines unless they interact with matter.
• 15.1.A.3 The speed of a photon depends on the medium through which the photon travels.
  • 15.1.A.3.i The speed of all photons in free space is equal to the speed of light, $c = 3.00 \times 10^{8}$ m/s.
  • 15.1.A.3.ii In general, the speed of photons through a given medium is inversely proportional to the index of refraction of that medium.
• 15.1.A.4 Particles can demonstrate wave properties, as shown by variations of Young's double-slit experiment.
  • 15.1.A.4.i A wave model of matter is quantified by the de Broglie wavelength, which increases as the momentum of a particle decreases.
    • Relevant equation:
    • $\lambda = \dfrac{h}{p}$
  • 15.1.A.4.ii Quantum theory is necessary to describe systems where the de Broglie wavelength is comparable to the size of the system.
• 15.1.A.5 Values of energy and momentum have discrete, or quantized, values for bound systems described by quantum theory.

Learning Objective 15.2.A: Describe the properties of an atom.

• 15.2.A.1 Atoms have internal structure.
  • 15.2.A.1.i Atoms consist of a small, positively charged nucleus surrounded by one or more negatively charged electrons.
  • 15.2.A.1.ii The nucleus of an atom is made up of protons and neutrons.
  • 15.2.A.1.iii The number of neutrons and protons in an atom can be represented using nuclear notation.
  • 15.2.A.1.iv An ion is an atom with a nonzero net electric charge.
• 15.2.A.2 Each atomic element has a unique number of protons.
  • 15.2.A.2.i The number and arrangements of electrons affects how atoms interact.
  • 15.2.A.2.ii The total number of neutrons and protons identifies the isotope of an element.
  • 15.2.A.2.iii The mass of an atom is dominated by the total mass of the protons and neutrons in its nucleus.
• 15.2.A.3 The Bohr model of the atom is based on classical physics and was the historical representation of the atom that led to the description of the hydrogen atom in terms of discrete energy states.
  • 15.2.A.3.i In the Bohr model of the atom, electrons are modeled as moving around the nucleus in circular orbits determined by the electron's charge and mass, as well as the electric force between the electron and the nucleus.
    • Relevant equations:
    • $F_e = k\dfrac{q_1 q_2}{r^2}$
    • $F_{\text{net}} = m\dfrac{v^2}{r}$
  • 15.2.A.3.ii The standing wave model of electrons accounts for the existence of specific allowed energy states of an electron in an atom, because the electron orbit's circumference must be an integer multiple of the electron's de Broglie wavelength.

Boundary statement: The analysis and description of electron structure is limited to energy levels and will not include such advanced descriptions as orbitals, orbital shapes, or probability functions.

Learning Objective 15.3.A: Describe the emission or absorption of photons by atoms.

• 15.3.A.1 Energy transfer occurs when photons are absorbed or emitted by an atom, which is modeled as a system consisting of a nucleus and an electron.
• 15.3.A.2 Energy can only be absorbed or emitted by an atom if the amount of energy being absorbed or emitted corresponds to the energy difference between two atomic energy states.
  • 15.3.A.2.i An atom in a given energy state may absorb a photon of the appropriate energy and transition to a higher energy state.
  • 15.3.A.2.ii An atom in an excited energy state may emit a photon of the appropriate energy to spontaneously move to a lower energy state.
  • 15.3.A.2.iii Because an atom is modeled as a system consisting of an electron and a nucleus, a change in the energy state of an atom corresponds to a change in the interaction energy between the electron and the nucleus.
• 15.3.A.3 Transitions between two energy states of an atom correspond to the absorption or emission of a photon of a single frequency and, therefore, a single wavelength.
• 15.3.A.4 Atoms of each element have a unique set of allowed energy levels and thereby a unique set of absorption and emission frequencies. The unique set of frequencies determines the element's spectrum.
  • 15.3.A.4.i An emission spectrum can be used to determine the elements in a source of light.
  • 15.3.A.4.ii An absorption spectrum can be used to determine the elements composing a substance by observing what light the substance has absorbed.
  • 15.3.A.4.iii Energy level diagrams are commonly used to visually represent the energy states of an atom.
• 15.3.A.5 Binding energy is the energy required to remove an electron from an atom, causing the atom to become ionized. An atom in the lowest energy level (ground state) will require the greatest amount of energy to remove the electron from the atom.

Boundary statement: In AP Physics 2, only energy level diagrams of single-electron atoms will be considered.

Learning Objective 15.5.A: Describe an interaction between photons and matter using the photoelectric effect.

• 15.5.A.1 The photoelectric effect is the emission of electrons when electromagnetic radiation is incident upon a photoactive material.
• 15.5.A.2 The emission of electrons via the photoelectric effect requires a minimum frequency of incident light, called the threshold frequency.
  • 15.5.A.2.i Light that is incident on a material and is at the threshold frequency or higher will induce electron emission, regardless of the number of photons that strike the material.
  • 15.5.A.2.ii The energy of the emitted electrons is not dependent on the number of photons that are incident upon the material, which provides evidence that light is a collection of discrete, quantized energy packets called photons.
• 15.5.A.3 The maximum kinetic energy of an emitted electron is related to the frequency of the incident light and the work function of the material, $\phi$.
  • 15.5.A.3.i The work function of a material is the minimum energy required to emit an electron from atoms in the material.
  • 15.5.A.3.ii The maximum kinetic energy of an emitted electron is given by the equation $K_{\max} = hf - \phi$.
  • 15.5.A.3.iii In a typical experimental setup to demonstrate the photoelectric effect and determine the work function of a metal, two metal plates are placed in a vacuum chamber and connected to a variable source of potential difference. One of the plates is illuminated by monochromatic light that causes electrons to be ejected and the potential difference between the plates is adjusted until no current is measured in the circuit.

Boundary statement: Where applicable, work functions for materials will be provided on the exam; students are not expected to know values of work functions or variables of a material that influence the magnitude of its work function.

Learning Objective 15.6.A: Describe the interaction between photons and matter using Compton scattering.

• 15.6.A.1 In Compton scattering, a photon interacts with a free electron. The Compton effect is when a photon that emerges from the interaction has a lower energy and longer wavelength than the incoming photon. The magnitude of the change is related to the direction of the photon after the collision.
• 15.6.A.2 Compton scattering provides evidence that light is a collection of discrete, quantized energy packets called photons.
  • 15.6.A.2.i Compton scattering can be explained by treating a photon as a particle and applying conservation of energy and conservation of momentum to the collision between the photon and electron.
  • 15.6.A.2.ii The transfer of a photon's energy to an electron results in the energy, momentum, frequency, and wavelength of the photon changing.
    • Relevant equations:
    • $E = hf$
    • $\lambda = \dfrac{h}{p}$
• 15.6.A.3 The change in wavelength experienced by a photon after colliding with an electron is related to how much the photon's direction changes.
  • Relevant equation:
  • $\Delta\lambda = \dfrac{h}{m_e c}(1 - \cos\theta)$

Boundary statement: AP Physics 2 includes full quantitative and qualitative treatments of conservation of momentum in two dimensions.

Learning Objective 15.7.A: Describe the physical properties that constrain the behavior of interacting nuclei, subatomic particles, and nucleons.

• 15.7.A.1 The strong force is exerted at nuclear scales and dominates the interactions of nucleons (protons or neutrons).
• 15.7.A.2 Possible nuclear reactions are constrained by the law of conservation of nucleon number.
• 15.7.A.3 The behavior of the constituent particles of a nuclear reaction is constrained by laws of conservation of energy, energy-mass equivalence, and conservation of momentum.
• 15.7.A.4 For all nuclear reactions, mass and energy may be exchanged due to mass-energy equivalence.
  • Relevant equation:
  • $E = mc^2$
• 15.7.A.5 Energy may be released in nuclear processes in the form of kinetic energy of the products or as photons.
• 15.7.A.6 Nuclear fusion is the process by which two or more smaller nuclei combine to form a larger nucleus, as well as subatomic particles.
• 15.7.A.7 Nuclear fission is the process by which the nucleus of an atom splits into two or more smaller nuclei, as well as subatomic particles.
• 15.7.A.8 Nuclear fission may occur spontaneously or may require an energy input, depending on the binding energy of the nucleus.

Learning Objective 15.7.B: Describe the radioactive decay of a given sample of material consisting of a finite number of nuclei.

• 15.7.B.1 Radioactive decay is the spontaneous transformation of a nucleus into one or more different nuclei.
  • 15.7.B.1.i The time at which an individual nucleus undergoes radioactive decay is indeterminable, but decay rates can be described using probability
  • 15.7.B.1.ii The half-life, $t_{1/2}$, of a radioactive material is the time it takes for half of the initial number of radioactive nuclei to have spontaneously decayed.
  • 15.7.B.1.iii The decay constant $\lambda$ can be related to the half-life of a radioactive material with the equation $\lambda = \dfrac{\ln 2}{t_{1/2}}$.
• 15.7.B.2 A material's decay constant may be used to predict the number of nuclei remaining in a sample after a period of time, or the age of a material if the initial amount of material is known.
  • Relevant equation:
  • $N = N_0 e^{-\lambda t}$
  • Derived equation:
  • $\ln\left(\dfrac{N}{N_0}\right) = -\lambda t$
• 15.7.B.3 Different unstable elements and isotopes may have vastly different half-lives, ranging from fractions of a second to billions of years.

Learning Objective 15.8.A: Describe the processes by which individual nuclei decay.

• 15.8.A.1 Some processes by which nuclei decay emit subatomic particles with unique properties.
  • 15.8.A.1.i An alpha particle, or helium nucleus, consists of two neutrons and two protons and is symbolized by $\alpha$ or $\text{He}^{2+}$. (In Physics 2, only He-4 nuclei will be considered.)
  • 15.8.A.1.ii Neutrinos and antineutrinos are subatomic particles that have no electrical charge, have negligible mass, and are symbolized by $\nu$ and $\bar{\nu}$, respectively.
  • 15.8.A.1.iii Neutrinos and antineutrinos only interact with matter via the weak force and the gravitational force, which results in very little interaction with normal matter.
  • 15.8.A.1.iv Positrons, or antielectrons, are subatomic particles that have an electric charge opposite that of an electron, have the same mass as an electron, and are symbolized by $e^+$ or $\beta^+$.
• 15.8.A.2 Nuclei can undergo radioactive decay via alpha decay, beta-minus decay ($\beta^-$), beta-plus decay ($\beta^+$), and gamma decay ($\gamma$).
  • 15.8.A.2.i In all nuclear decays, nucleon number (the number of neutrons and protons), lepton number (the number of electrons and neutrinos), and charge are conserved.
  • 15.8.A.2.ii Alpha decay occurs when a nucleus ejects an alpha particle.
  • 15.8.A.2.iii Beta-minus decay occurs when a neutron changes to a proton by emitting an electron and antineutrino.
  • 15.8.A.2.iv Beta-plus decay occurs when a proton changes to a neutron by emitting a positron and neutrino.
  • 15.8.A.2.v Gamma decay occurs after a nucleus has undergone alpha or beta decay and the excited nucleus decays to a lower energy state by emitting a photon.
• 15.8.A.3 The type of decay exhibited by a given nucleus is determined by the isotope of the element.

Boundary statement: AP Physics 2 does not expect students to memorize the processes by which specific isotopes decay or the half-lives of specific isotopes. Neutron emission and electron capture are not included in the AP Physics 2 curriculum framework. Additionally, types of neutrinos, the characteristics that distinguish neutrinos and antineutrinos, and an explanation or application of the weak force are not within the scope of this course.