Category: Part 6: Atomic & Nuclear

Problem Statement Solve the nuclear physics problem: Solve the nuclear physics problem: A nucleus can decay by alpha ($\lambda_\alpha$) or beta ($\lambda_\beta$) emission. Find the total half-life and the branching fractions. When multiple decay channels are available, the total decay constant is the sum: $$\lambda_{total} = \lambda_\alpha + \lambda_\ Given Information Nuclide symbol, atomic number…

Problem Statement Problem 6.119 — Hyperfine Structure: 21 cm Hydrogen Line 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…

Problem Statement Problem 6.183 — Beta Spectrum: Fermi Theory 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…

Problem Statement Solve the quantum/modern physics problem: Problem 6.127 — Quantum Confinement: Quantum Dot $= \frac{3\times1.047\times10^{-67}}{1.822\times10^{-46}} = 1.72\times10^{-20} \text{ J} = 0.107 \text{ eV}$ $E_{211} = \frac{\pi^2\hbar^2}{2m_eL^2}(4+1+1) = 2E$ This problem applies fundamental physics principles to the scenario described. The soluti Given Information Frequency $\nu$ or wavelength $\lambda$ of radiation Work function $\phi$ of metal…

Problem Statement Problem 6.118 — Schrödinger Equation: Delta Function Potential 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 nuclear physics problem: Problem 6.182 — Alpha Decay: Velocity and Range $= \sqrt{2.41\times10^{14}} = 1.55\times10^7 \text{ m/s} = 0.052c$ $R = 0.31\times(5.0)^{3/2} = 0.31\times11.18 = 3.47 \text{ cm}$ Projectile motion decomposes into independent horizontal and vertical components. Horizontal: constant velocity (no air r Given Information Nuclide symbol, atomic number $Z$, mass…

Problem Statement Problem 6.126 — Hydrogen: Paschen Series 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 Problem 6.125 — Dirac Equation: Electron Spin 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…

Problem Statement Solve the oscillation/wave problem: Problem 6.124 — Three-Dimensional Harmonic Oscillator 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 w Given Information Mass $m$ and spring constant $k$ (or equivalent),…

Problem Statement Problem 6.117 — Thomas-Fermi Model 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…