Category: Part 6: Atomic & Nuclear

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: Describe Einstein’s explanation of the photoelectric effect and why it required quantization of light. Classical wave theory predicted: Any frequency should eject electrons (given enough intensity) Higher intensity → higher electron energy There should be a Given Information Frequency $\nu$ or wavelength $\lambda$…

Problem Statement Solve the nuclear physics problem: $^{235}$U fission releases on average $\bar{\nu} = 2.43$ neutrons per fission. Most are prompt; 0.65% are delayed. Explain the role of delayed neutrons in reactor control. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Given Information Nuclide symbol,…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: Problem 6.133 — Photon Scattering: Thomson and Compton 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 equatio Given Information Frequency $\nu$ or wavelength $\lambda$ of…

Problem Statement Derive the Stefan-Boltzmann law $P = \sigma T^4$ by integrating Planck’s formula. 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…

Problem Statement Solve the nuclear physics problem: In $^{235}$U fission, the most probable fragment masses are around $A \approx 95$ and $A \approx 140$. Why is the distribution asymmetric? All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws on fundamental Given Information Nuclide…

Problem Statement Find the minimum electron kinetic energy needed to ionize a helium atom from the ground state (first ionization energy = 24.6 eV). 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.…

Problem Statement Solve the nuclear physics problem: Solve the nuclear physics problem: A deformed nucleus rotates. If the first excited state of $^{168}$Er ($J^\pi = 2^+$) is at 79.8 keV, find the nuclear moment of inertia. For a rigid rotor, the rotational energy levels are: $$E_J = \frac{\hbar^2}{2\mathcal{I}}J(J+1)$$ The $2^+ \to 0^+$ transition e Given…

Problem Statement Solve the quantum/modern physics problem: Solve the work-energy problem: A metastable state has lifetime $\tau = 1$ ms. Find the energy uncertainty and the minimum linewidth. $$\Delta E = \hbar/\tau = 1.055\times10^{-34}/10^{-3} = 1.055\times10^{-31} \text{ J} = 6.6\times10^{-13} \text{ eV}$$ $$\Delta\nu = \Delta E/h = 1/(2\pi\tau) = 159 \t Given Information Frequency $\nu$…

Problem Statement The Geiger-Nuttall law states $\log_{10}T_{1/2} = a + b/\sqrt{E_\alpha}$ for alpha decay. Using two data points for uranium isotopes, find $a$ and $b$: $^{234}U$: $T_{1/2} = 2.46\times10^5$ yr, $E_\alpha = 4.858$ MeV; $^{238}U$: $T_{1/2} = 4.47\times10^9$ yr, $E_\alpha = 4.270$ MeV. Given Information All quantities, constants, and constraints stated in the problem above…

Problem Statement Explain the physical significance of the fine structure constant $\alpha = e^2/(4\pi\varepsilon_0\hbar c) \approx 1/137$. 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…