Category: Part 6: Atomic & Nuclear

Problem Statement Problem 6.157 — Carbon-14 Dating Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system, then apply it…

Problem Statement Problem 6.100 — Ehrenfest’s Theorem Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system, then apply it…

Problem Statement Problem 6.93 — Variational Principle: Hydrogen Ground State Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system,…

Problem Statement Solve the quantum/modern physics problem: Problem 6.92 — Hydrogen Atom: Quantum Numbers and Spectroscopic Notation See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solvi Given Information Frequency $\nu$ or wavelength $\lambda$…

Problem Statement Solve the nuclear physics problem: Problem 6.156 — Radioactive Decay: Activity and Half-life $T_{1/2} = \ln2/\lambda = 0.6931/$ This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with caref Given Information Nuclide symbol, atomic number $Z$, mass…

Problem Statement Solve the oscillation/wave problem: Problem 6.99 — Hydrogen Wavefunction: Node Structure See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically wi Given Information Mass $m$ and spring constant $k$ (or…

Problem Statement Problem 6.98 — Pauli Exclusion Principle Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system, then apply…

Problem Statement Solve the nuclear physics problem: Problem 6.155 — Radioactive Decay Law $N_0/2 = N_0 e^{-\lambda T_{1/2}} \implies T_{1/2} = \ln2/\lambda = 0.693/$ $\tau = \int_0^\infty t\lambda e^{-\lambda t}dt = 1/$ This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conser Given Information Nuclide symbol, atomic number…

Problem Statement Problem 6.91 — WKB Approximation Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system, then apply it…

Problem Statement Solve the nuclear physics problem: The charge radius of a nucleus scales as $R = R_0 A^{1/3}$ with $R_0 = 1.2$ fm. Find the radius of $^{208}$Pb. $$R = R_0 A^{1/3} = 1.2 \times (208)^{1/3} = 1.2 \times 5.927 = 7.11 \text{ fm}$$ Nuclear density (uniform sphere approximation): $$\rho = \frac{A\times m_u}{(4/3)\pi R^3}…