Category: Part 6: Atomic & Nuclear

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: Explain the measurement postulate and wavefunction collapse with a concrete example. Measurement postulate: Before measurement, a quantum system is in a superposition of eigenstates. Upon measurement of observable $\hat{A}$: The probability of obtaining eigenvalue Given Information Mass $m$ and spring constant $k$ (or equivalent), or…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: At what photon energy does the Compton cross section equal the Thomson cross section? The Thomson cross section (classical limit, low energy): $$\sigma_T = \frac{8\pi}{3}r_e^2 = \frac{8\pi}{3}\left(\frac{e^2}{4\pi\varepsilon_0m_ec^2}\right)^2 = 6.65\times10^ Given Information Frequency $\nu$ or wavelength $\lambda$ of radiation Work function $\phi$ of metal…

Problem Statement Find the wavelengths of the first three lines of the Paschen series ($n_f = 3$). 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…

Problem Statement Solve the nuclear physics problem: Solve the magnetic field/force problem: Find the resonance frequency for proton NMR at $B = 7.05$ T (the proton gyromagnetic ratio $\gamma_p = 2.675\times10^8$ rad/T·s). The proton magnetic moment precesses around $\mathbf{B}$ at the Larmor frequency: $$\omega_L = \gamma_p B = 2.675\times10^8\times7 Given Information Nuclide symbol, atomic number…

Problem Statement Explain how the Dirac equation naturally predicts electron spin and the $g$-factor $g_s = 2$. 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…

Problem Statement Find the Q-value for electron capture (EC) in $^{65}$Zn: $^{65}$Zn + $e^- \to ^{65}$Cu + $\nu_e$. Masses: $M(^{65}Zn) = 64.92924$ u, $M(^{65}Cu) = 64.92778$ u. 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…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: Find the energy levels and degeneracies of a 3D isotropic harmonic oscillator. The 3D oscillator separates into three 1D oscillators: $$E_{n_x,n_y,n_z} = \hbar\omega(n_x + n_y + n_z + 3/2) = \hbar\omega(N + 3/2)$$ where $N = n_x + n_y + n_z = 0, 1, 2,…

Problem Statement Explain internal conversion. The $K$-shell internal conversion coefficient for a $^{197}$Au transition is $\alpha_K = 3.3$. Find the intensity ratio of conversion electrons to gamma rays. 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…

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 Find the polarizability of the hydrogen atom in the ground state from the second-order Stark effect. 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…