Category: Part 6: Atomic & Nuclear

Problem Statement Identify the hydrogen transition at $\lambda = 486.0$ nm. 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 Express $R_\infty$ in terms of fundamental constants and calculate its value. 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…

Problem Statement Solve the momentum/collision problem: Solve the momentum/collision problem: Show that Bohr’s quantization follows from fitting integer de Broglie wavelengths into the orbit. Condition: $2\pi r = n\lambda_{dB} = nh/(m_ev)$ $$L = m_evr = m_ev\cdot\frac{nh}{2\pi m_ev} = n\hbar$$ This is Bohr’s angular momentum quantization: $L_n = n\hbar$. Given Information Masses $m_1$, $m_2$ and initial…

Problem Statement X-rays of $\lambda = 0.150$ nm ionize hydrogen. Find the photoelectron kinetic energy. 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…

Problem Statement Solve the oscillation/wave problem: Solve the nuclear physics problem: Find the $K_\alpha$ X-ray wavelength for (a) Al ($Z=13$), (b) Co ($Z=27$). $E_{K_\alpha} = 10.2(Z-1)^2$ eV: (a) Al: $10.2\times144 = 1469$ eV, $\lambda = 1240/1469 = 0.845$ nm (b) Co: $10.2\times676 = 6895$ eV, $\lambda = 1240/6895 = 0.180$ nm Nuclide symbol, atomi Given…

Problem Statement Solve the work-energy problem: Solve the nuclear physics problem: The K-absorption edge of silver is at $\lambda_K = 0.0485$ nm. Find the K-shell binding energy. $$E_K = hc/\lambda_K = 1240 \text{ eV·nm}/0.0485 \text{ nm} = 25567 \text{ eV} \approx 25.6 \text{ keV}$$ Answer: $E_K \approx 25.6$ keV Nuclide symbol, atomic number $Z Given…

Problem Statement Find the first Bohr radius and ionization energy for muonic hydrogen ($m_\mu = 207m_e$). 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…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Find the energy levels and first Bohr radius of positronium (electron + positron). Reduced mass: $\mu = m_e/2$. Energy and radius scale with $\mu/m_e$: $$E_n^{Ps} = -\frac{6.8 \text{ eV}}{n^2}, \quad a_0^{Ps} = 2a_0 = 1.058 \text{ Å}$$ Ionization energy = 6.8 eV; Ly-$\ Given Information…

Problem Statement Verify wavelengths 656.3, 486.1, 434.0, 410.2 nm as Balmer series using the Rydberg 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…

Problem Statement Mercury current drops at 4.9 V, 9.8 V, 14.7 V in Franck-Hertz. Find the emitted photon wavelength. 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…